|From what you state it sounds like the drive is probably OK. While on the subject of the drive there is a setting in the BIOS called S.M.A.R.T. This setting monitors the drive parameters and reports if anything gets too far out of wack. SMART may be disabled in the BIOS.|
I think your problem is a hardware issue.
Open your case and re-seat ALL cards and cables. Remove and reinstall the RAM sticks 4 or 5 times each. If that doesn't solve the problem download and run from a boot disk, memtest86.
The fact that the computer runs after 30 minutes kind of indicates to me a bad connection. Possible that the power supply is also at fault.
If the issue persists you can try to isolate it by disconnecting peripheral hardware and if that doesn't help start disabling integrated hardware, one by one, as allowable.
Also visually check the motherboard for any bulging or leaking capacitors.
Something I forgot to ask. When you start the computer is the monitor light yellow or green?