Safari keeps saying it can't establish a secure connection to the server

If your computer is a 2010 computer, you can upgrade to at least El Capitan and possibly higher. I would do the factory reset suggested by Kappy before doing anything.

Check that your computer is compatible with Mountain Lion/Mavericks/Yosemite/El Capitan.

To check the model number hold down the option/alt key, go to the Apple menu and select System Information.

MacBook (Late 2008 Aluminum, or Early 2009 or newer) model number 5,1 or higher

MacBook Pro (Mid/Late 2007 or newer) model number 3,1 or higher

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Your Mac needs:

OS X v10.6.8 or OS X Lion already installed

2 GB or more of memory (More is better - 4 GB minimum seems to be the consensus)

8 GB or more of available space

Check to make sure your applications are compatible.

Application Compatibility

El Capitan 10.11 Compatibility information

macOS Sierra 10.12: Compatible Apps

Also check to make sure there is a compatible driver for your printer.

Do a backup before installing, preferable 2 backups on 2 different drives.

macOS 10.12 (Sierra) requires one of the following Macs:

MacBook (Late 2009 or later) Model 6.1 and higher

MacBook Pro (Mid 2010 or later) Model 6.2 and higher

How to get macOS High Sierra

Sierra download

You can try to download it at the link below. If it won't let you, then your only options are to upgrade to Sierra/High Sierra or find an older computer where you can download it using your Apple ID.

El Capitan

You need to do this:

How To Do A Factory Reset

Selection A should be used on computers that came with Lion or later when factory new. These models had no disks included when new. Selection B is for Macs that came originally with Snow Leopard or earlier. These models shipped with Software Restore disks when new.

A. Factory reset of your Mac - Apple Support

B. Factory Reset Your Pre-Lion Mac

Follow these instructions until you get to Step 5: Factory reset of your Mac - Apple Support. At Step 5 you will need a Snow Leopard DVD or the installer disc that came with the computer.

1. Boot the computer using the Snow Leopard Installer Disc or the Disc 1 that came with your computer. Insert the disc into the optical drive and restart the computer. After the chime press and hold down the "C" key. Release the key when you see a small spinning gear appear below the dark gray Apple logo.
2. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Utilities' menu. After Disk Utility loads select the hard drive entry from the left side list (un-dented entry - mfgr.'s ID and drive size.) Click on the Partition tab in the Disk Utility main window. Set the number of partitions to one (1) from the Partitions drop down menu, click on Options button and select GUID, click on OK, then set the format type to MacOS Extended (Journaled), then click on the Apply button.
3. When the formatting has finished quit Disk Utility. Proceed with the OS X installation and follow the directions included with the installer.
4. If you are planning to sell or give your computer away, then do the following: After you reformat your hard drive and reinstall OS X, the computer restarts to a Welcome screen and asks you to choose a country or region. If you want to leave the Mac in an out-of-box state, don't continue with the setup of your system. Instead, press Command-Q to shut down the Mac. When the new owner turns on the Mac, the Setup Assistant will guide them through the setup process.