I previously suggested a failing power supply. That is still a very real possibility. That's on the hardware side.

On the software side, you may have been visited by a nasty. As has been suggested, Malwarebytes is an excellent program, a free program.

Malwarebytes

Another free program I would recommend is Superantispyware.

Superantispyware

A third is TrendMicro Housecall.

HouseCall

No single program will root out all the nasties. Using multiple programs is well worth the effort. These three are IN ADDITION to a regular, always active, antivirus.

Another possibility on the hardware side is capacitors. Your system might have capacitors going bad. My other daughter had this happen to her on a good quality Abit motherboard. Read about this problem.

BadCaps

That should keep you busy for a bit. Running any of these diagnostic programs depends on the system staying up long enough. Running them in Safe Mode is recommended, and your best bet.