MacBook Pro not logging in after installation of OS X El Capitan.

Try this:

Reinstall El Capitan or Later Without Erasing Drive

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.

Then you will have to try my original procedure that does not erase the drive. I'm concerned, though, that you may not succeed with it given that what you now have does not work as it should. You cannot repair an installed system that has failed as suggested by the kernel panic. Nevertheless, you can give it a try. The worse that can happen is it won't work.

If you need to recover your data because you don't have a backup and you cannot install macOS unless you erase the disk which will result in erasing your files, then you need to connect your computer to another Mac which has the same connection ports. Then you may be able to access your drive from another Mac that is connected to yours, by using Target Disk Mode. Also, see How to use target disk mode to move files between two Mac computers, How to use target disk mode to move files between two Mac computers and Using Target Disk Mode to install an operating system.

Reinstall El Capitan or Later Without Erasing Drive

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.

That is a kernel panic screen. It seems to have occurred because your computer is trying to start from an incomplete system as a result of shutting down during the installation. You need to perform the full installation process a bit differently. You cannot re-install over a defective installation. This time you will have to erase the disk. Here are the two basic procedures you can use. The first one requires a working Recovery HD. If you cannot boot from the Recovery HD, then you will need to perform a Network Recovery. That will the the second one.

Install El Capitan or Later from Scratch from Recovery HD

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 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) 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.

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

     If possible back up your files before proceeding.

1. Restart the computer. Immediately after 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 (will be the out-dented entry) 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) or Mac OS Extended (Journaled.)
8. Click on the Apply button, then click on the Done button when it activates.
9. Quit Disk Utility and return to the Utility Menu.
10. Select Install OS X and click on the Continue button.

If you have not yet started the installation, then you can simply reboot the computer without making any changes. The reboot option is under the Apple menu in the screen menubar.