Q: Failed El Capitan update on early 2011 MacBook Pro,

Try this:

Boot the computer into Safe Mode, then restart normally. This will be slower than a normal startup.

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

Resetting your Mac's PRAM and NVRAM

Repair the Hard Drive and Permissions - El Capitan

Boot to the Recovery HD:

Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears.

Repair

When the recovery menu appears select Disk Utility and press the Continue button. After Disk Utility loads select the indented Macintosh HD entry from the the left side list.  Click on the First Aid tab in the toolbar.. If Disk Utility reports any errors that have been fixed, then re-run First Aid until no errors are reported. Wait until the operation completes, then quit Disk Utility and return to the main menu. Select Restart from the Apple menu.

Now, Download and Reinstall OS X El Capitan 10.11.3 Combo Update.