As mentioned before - you are likely getting into a thermal situation. Take the box outside and blow out any dust that has collected especially around heat sinks and the power supply. Test again.
If this is still happening - remove all drives except your C: drive. If you have onboard Video - remove any video cards and other peripherals. Test again.
If the problem goes away – start adding components back in until it re-occurs. Note you have not fixed anything yet – just limiting the power draw and slowly increasing it. If the problem occurs before you get all your bits back in – then the last bit you added was the tipping point, or one of the recently added components is faulty. Assuming it was a tipping point – figure out the...