For the fact that it shuts down like that here are possible shutdown causing conditions:
Overclock is on the edge of running correctly and failure ( unstable ) * Resetting the BIOS should undo all overclocks
Power Supply Issue ---- Check voltages, in the BIOS it might tell you what your voltages are, you can also verify the 5V and 12V with a multimeter if you know how to do that safely. A weak power supply will cause the system to fail to boot when power is needed the most at boot.
Temperature Issue ----- * Usually systems with this problem will run fine until hot, so symptoms are a running system that gets hot and shuts down. Then turn it back on and it has cooled so it runs again until overheat.
CPU fan issue ( stops spinning and tach failure )
RAM ( flakey memory ) ----- Test RAM with Memtest86
Video Card overheating causing a GPF BSOD and reboot or shutdown * Usually you dont get the POS beep with these unless the card is fried. If the card is fried usually it doesnt get out of the POST beep condition.
motherboard is dying ( capacitors or VRMs stressed etc ) * Look for capacitors that may be leaking, inspect the main board for an area that might have a strong electronic smell or discoloration from excessive heat..Not all failures are visually found, but sometimes they can be.
The BIOS Beep Code as Allan suggested looking into, should pinpoint what the motherboard is crying about for failure. There are long and short beeps. If its a quick Beep Beep Beep its one code if its a Long Beep and 2 short Beeps its another etc. So you need to know the duration of the 3 beeps whether long to short beeps as for that makes a difference in what is reported by the main board.
