|"PC likes to restart on its own a lot"|
This is more of a problem, I'd work on it first.
The beep may be power supply, would be my guess. Try a known good one.
Might be that the computer is actually sending a fault but kind of hard to tell, I doubt the event view would show an issue. Might look at it. Might look at dump logs too.
"Best Practices", Event viewer, host file, perfmon, antivirus, anti-spyware, Live CD's, backups, are in my top 10