It might be a temperature related issue. If the PC was stored or a bit of time, I'd blow out all of the old dirt/dust. I'd boot the system into the BIOS and watch/monitor the temperatures (mainly the CPU) and see if it can stay stable for 20-30 min. If it doesn't stay stable and is continually rises in temperature, than you might have a CPU HSF connection issue. This would require pulling off the CPU HSF and cleaning off the thermal paste off of the CPU and the CPU HSF. Then re-apply some new paste and repeat the thermal test in the BIOS.
If you temperatures are stable, than I'd look at the voltages in the BIOS too. This might show you whether or not your PSU is outputting the correct voltages to your computer parts. If it isn't, than you'd know that you need to replace the PSU.