My first guess would be heat. Open the case and clean out all dust, I use a camera brush and a small fan to blow everything clear of the case. Pay close attention to the fins of the CPU heat sink, and be careful. A can of compressed air from Radio Shack will blow any leftover dust clear.
Then leave the case open, and set up the computer, place a small fan so it can blow into the case while it runs. Keep the cat out of the room... hehe...Try it for a day or 2 and see what happens. If it runs ok, put the cover back on and try it. If the problem starts again, try putting the fan where it can blow into the area where the computer sits, especially if this is an enclosed cabinet area in a desk. You can get extra case fans at computer shops, or CSO and they're not more than about $10. If you try and install one, make sure it moves air the same direction as the existing power supply fan does. Most cases have a secondary fan mount, but most companies are too cheap to put one in it.
By the way, check to see that the power supply and CPU fans are both working...and clean...
If it turns out to be heat, you might need move the computer to a different location where it can get better airflow. I hate to say it, but heat problems can also damage the CPU and power supply...
If it's not heat, those are the most likely culprits.
If you had everything...Where would you put it?
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