Sounds like a heat issue, or a cpu that does not have adequate thermal paste between heat sink and cpu fan.
It is old enough to require a replacement hard drive... Good to test with another hard drive.
Is the screen any different when booted to SAFE MODE?
Do you have a separate video graphics card, or is it connected to onboard graphics?
Power supply could be failing. A power supply tester costs $10 to $15 on up to $15, but just exchanging with another power supply would satisfy that inquiry.
Other items to consider on that model: CMOS battery might be failing.
One simply test is to remove and reseat all cables. Consider replacing the EIDE 80 Connector 40 conductor cable from board to hard drive.
Clean all dust, dirt, fiber and hair out of the heat sink, if not already done.