PC shuts down and restarts after several minutes running

Hi ,can anyone help me with the following problem?
A PC running XP runs when started from cold for between 5 and 20 minutes before switching off and attempting to restart.At restart there is power to the motherboard ,fans and all drives but no activity from the ide or onboard graphics ,also the PC does not appear to be going through the POST routine (no beeps etc).CMOS battery OK,replaced power supply – made no difference.While PC is running diagnostics say Celeron 330 is running at 28/29degrees C.
New motherboard due ?

Thanks
John