Q: Dead screen after downloading El Capitan OSX

How long has it been running that way?

- Try resetting the SMC and NVRAM/PRAM

Intel-based Macs: Resetting the System Management Controller (SMC)

https://support.apple.com/en-us/HT201295

About NVRAM and PRAM 

https://support.apple.com/en-us/HT204063

- Try starting in Safe Mode

OS X: What is Safe Boot, Safe Mode?

https://support.apple.com/en-us/HT201262

- Boot to Recovery and repair the startup disk

OS X: About OS X Recovery - Apple Support

https://support.apple.com/en-us/HT201314

- If it is repairable reinstall the OSX

How to reinstall OS X on your Mac - Apple Support

https://support.apple.com/en-us/HT204904

- If you do not have a backup use disk utility to restore the internal disk to an external disk so you can try to recover data.

Do you have silver tower, 40 lb Mac Pro or a MacBook Pro? This is the Mac Pro desktop forum?

Try these in order testing your system after each to see if it's back to normal:

1.  a. Resetting your Mac's PRAM and NVRAM

     b. Intel-based Macs: Resetting the System Management Controller (SMC)

2. Restart the computer in Safe Mode, then restart again, normally. If this doesn't help, then:

     Boot to the Recovery HD: Restart the computer and after the chime press and hold down the

     Command and R keys until the Utility Menu screen appears.

3. Repair the Hard Drive and Permissions: Restart the computer and after the chime press and hold down the Command and R keys until the Utility Menu screen appears.

    When the Utility Menu appears select Disk Utility and press the Continue button. After Disk Utility loads select the

    indented (usually, Macintosh HD) entry from the the side list.  Click on the First Aid button in the toolbar. Wait until the operation

    completes, then quit Disk Utility and return to the Utility Menu.

4. Download and Install the OS X El Capitan 10.11.5 Combo Update.

5. Reinstall OS X: Reboot from the Recovery HD. Select Reinstall OS X from the Utility Menu, and click on the Continue button.

[Permission to use part or all of the above has been granted by Kappy, exclusively, to theratter.]