I got the "no" sign upon starting up and now my computer is acting odd.

If your Mac starts up to a circle with a line through it

A Troubleshooting Procedure that may Fix Problems with macOS El Capitan or Later

You should try each, one at a time, then test to see if the problem is fixed before going on to the next.

    If possible, backup your files before proceeding.

1. Shutdown the computer and disconnect all third-party peripherals.
2. Wait 30 seconds before you restart the computer.
3. Resetting your Mac's PRAM and NVRAM
4. Reset the System Management Controller (SMC)
5. Reset your Startup Disk and Sound preferences, if needed, after resetting the PRAM.
6. Test in safe mode to see if the problem persists, then restart normally. See How  to  use  safe  mode  on  your  Mac.
7. Repair the disk by booting from the Recovery HD. Immediately after the chime hold down the Command and R keys until the Utility Menu appears. Choose Disk Utility and click on the Continue button. Select the indented (usually, Macintosh HD) volume entry from the side list.  Click on the First Aid button in the toolbar. Wait for the Done button to appear. Quit Disk Utility and return to the Utility Menu. Restart the computer from the Apple Menu.
8. Create a New User Account Open Users & Groups preferences. Click on the lock icon and enter your Admin password when prompted. On the left under Current User click on the Add [+] button under Login Options. Setup a new Admin user account. Upon completion log out of your current account then log into the new account. If your problems cease, then consider switching to the new account and transferring your files to it - Transferring files from one User Account to another.
9. Reinstall a Combo Updater  macOS Catalina 10.15.6  Combo  Update, macOS Mojave 10.14.6 Combo Update, macOS High Sierra 10.13.6 Combo Update, macOOS 10.12.6 Combo Update, OS X El Capitan 10.11.6 Combo Update.
10. Reinstall OS X by booting from the Recovery HD using the Command and R keys. When the Utility Menu appears select Install OS X then click on the Continue button.
11. Erase and Install OS X Restart the computer. Immediately after the chime hold down the Command and R keys until the Apple logo appears. When the Utility Menu appears:

     1. Select Disk Utility from the Utility Menu and click on the Continue button.

     2. When Disk Utility loads select the drive (out-dented entry) from the Device list.

     3. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.

     4. Set the Format type to APFS (for SSDs only) or Mac OS Extended (Journaled.)

     5. Click on the Apply button, then wait for the Done button to activate and click on it.

     6. Quit Disk Utility and return to the Utility Menu.

     7. Select Install OS X and click on the Continue button.

If you are no longer able to step through the procedures in my earlier post, then you will need to resort to erasing the drive and reinstalling macOS. Unsecure website warnings are probably happening because your browser is out of date. You need to upgrade the OS. If you have an iMac from 2012 or later, then you would upgrade to Catalina 10.15.6.

To stay with El Capitan, you need to do the following assuming the Recovery Volume is still intact.

Install El Capitan or Later from Scratch

If possible, back up your files.

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility from the Utility Menu and click on the Continue button.
3. When Disk Utility loads select the target drive (out-dented entry w/type and size info) from the Device list.
4. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
5. Set the partition scheme to GUID.
6. Set the Format type to Mac OS Extended (Journaled.)
7. Click on the Apply button, then wait for the Done button to activate and click on it.
8. Quit Disk Utility and return to the Utility Menu.
9. Select Install OS X and click on the Continue button.

To upgrade to Catalina, you can do this:

Internet/Network Recovery of El Capitan or Later on a Clean Disk

     If possible, back up your files before proceeding.

You will need a fast, working Internet connection, preferably, Ethernet. If you must use Wi-Fi, you will be asked to select your network and enter the network password. This procedure will install the current version of macOS that is compatible with your model.

1. Restart the computer. Immediately, at or before the chime, hold down the (Command-Option-R) keys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the target drive (out-dented entry w/type and size) from the side list.
5. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to APFS (SSDs, only if installing Mojave or Catalina ) or Mac OS Extended, (Journaled.)
8. Provide a volume name, usually "Macintosh HD."
9. Click on the Apply button, then click on the Done button when it activates.
10. Quit Disk Utility and return to the Utility Menu.
11. Select Install OS X and click on the Continue button.

Before You Upgrade macOS

1. Fix any problems before upgrading or erase the drive.
2. Run First Aid in Disk Utility while booted from your Recovery HD.
3. Backup. Make a bootable clone using CarbonCopy Cloner or use TimeMachine.
4. Be sure your startup disk has 18-20GB of free space during the installation.
5. Upgrade third-party software for compatibility. See App Compatibility Table - RoaringApps. If you have mission critical software, then DO NOT upgrade until you know that software is compatible with the version of macOS you are about to install.
6. Disconnect all third-party peripherals.
7. Download the installer which will be in the Applications folder. Quit the installer after it opens, then make a copy of the installer and save it in the Downloads folder. The one in the Applications folder will be deleted after a successful installation.
8. The download is large, anywhere between 5 and 9GBs. It takes time to complete. Be patient.
9. Double-click on the installer in the Applications folder. Click on the start button to begin the installation.

You can give this a try:

Reinstall El Capitan or Later Without Erasing Drive

Please be sure you back up, if possible.

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility and click on the Continue button.
3. Select the indented (usually, Macintosh HD) volume entry from the side list.
4. Click on the First Aid button in Disk Utility's toolbar. Wait until the Done button activates, then click on it.
5. Quit Disk Utility and return to the Utility Menu.
6. Select Install OS X and click on the Continue button.

If you are not able to get this to work for you, then I'm afraid you are stuck with having to erase the startup volume. The following steps are similar to the previous ones, except for the added steps for erasing the startup volume.

Install El Capitan or Later from Scratch

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility from the Utility Menu and click on the Continue button.
3. When Disk Utility loads select the target volume (indented entry, usually "Macintosh HD") from the Device list.
4. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
5. Set the Format type to APFS (SSDs, only w/Mojave or Catalina) or Mac OS Extended (Journaled.)
6. Click on the Apply button, then wait for the Done button to activate and click on it.
7. Quit Disk Utility and return to the Utility Menu.
8. Select Install OS X and click on the Continue button.

If none of this works, then I'm afraid there is a hardware issue - could be the drive.

Haven't a clue. It's possible the drive is failing (is it a HDD or an SSD?) Perhaps, the drive's directory or a data block has been corrupted. The number of possibilities is large.

Hard for me to say since I'm not able to work directly with the computer, but it would seem that something is wrong. I'm not sure what that is, so the best bet is to take it in for service.

Make an appointment at the Apple Genius Bar for service after the stores re-open. If you need to find an Apple Store - Find a Store - Apple. Also, see How to find your nearest Apple Authorized Service Provider (AASP) or Distributor (AAD). You may also get Apple authorized service at a local Best Buy or contact Apple Support for more options.

Contacting Apple Customer and Support Service

1. Apple Store Customer Service at 1-800-676-2775 or visit online Help for more information.
2. To arrange a return for repair or replacement: Mac Repair.
3. If you just purchased the product, then you get 90 days of free telephone support from the date of purchase of your Apple product.
4. Primary support help at Contact Support.
5. To contact product and tech support: Contacting Apple for support and service including international calling numbers.
6. Product  Service  and  Repair  information.
7. Apple  Service  Programs.