My Mac Mini has two monitors and several USB devices plugged in. After the install, I got a black screen up on one of my monitors. As a result, I had to turn off the Mini with the power button on the back and it restarted with the Apple logo and then went to the black screen again. I decided to unplug all of the USB devices and keep only one monitor plugged in.
This time it restarted to a black screen, but down in the left corner, I saw a sliver of gray and I clicked on it. The multi-colored beachball came up on the screen, which was a great sign. A few minutes later, it was able to pull up my normal desktop. I didn't think that El Capitan installed because it did not change my desktop picture like it had on my other Macs. However, I went into the "About this Mac" settings and it was, in fact, updated.
Hopefully, you won't run into a similar issue, but if you do, hopefully this information will help.