Q: My computer stops booting about half way through the process.

Last night my computer restarted without my input.  When it was coming back up, it got to a point a little more than half way through, then stopped.  I tried numerous times to restart, but with the same results.  I tried doing the Apple Hardware Test (my computer is pre-2013) and my computer ignored the command to carry out the AHT.  I recently installed the El Capitan OS.  Is there a connection to my computer's recent irrational behavior?  Also, prior to this instance, my computer had restarted itself without my input several times.