Tell us a little more about thetype of computer, the type of CPU, amount of memory, type of memory.
The quick shutdown could be a CPU overheating fast, a bad Power supply, or possibly other things.
Is it an ATX type system??? Normally in ATX types the LED on the mobo indicated that the 5 volt standby power is present on the mobo. That voltage is ALWAYS there as long as the power supply is plugged into a live outlet and the switch on the rear of the power supply is ON. That power is always there whether you turn the computer off by windows or the front powewr switch.
Any other fans or lights to report about??
I have aquired a pc, quite basic but in very good nick, about 2-3 years old, but it will not boot up.
I currently have it open and when i try to boot up, the power supply fan, and main fan spin for 2-3 seconds, on the main board is a yellow led which activates for the same duration.