Computer starts up then shuts off.

Sounds like a heat problem, could be power supply.

Open the case, grab your heatsink, and gently but firmly try to rock it. If it moves, that's your problem. If it passes that test . . .

From a cold start, boot into BIOS, find the screen that shows "PC Health" or equivalent, and watch the temperature. If it climbs, shut down and remove/reinstall the heat sink properly.

If no temps in BIOS, use CPUID's Hardware Monitor.

It sounds like the cpu is overheating and shutting the system down.
-- First check your cpu fan while the system POSTing - does it continue to turn a rapid rate of speed? If not, check that the fan is properly connected to the CPU_FAN connector on the motherboard. If the fan turns and is properly connected to the board,
-- Check the heatsink to make sure it is firmly seated. If it is, you may have applied too little or too much thermal interface material (TIM) on the cpu or the heatsink, or both.
-- Review the TIM mfr's instructions for cleaning the heatsink base and the cpu, and for applying the compound. Try it again.
-- Run the system and check the cpu temps (CoreTemp, RealTemp, or another utility).

Thanks so much guys. it turns out that the problem was that when i changed the CPU's thermal paste i did not put enough so the heat was not transferring well enough and the computer was shutting down. this is why the time decreased after each attempt to start it because of the increasing heat and why it would take longer if left alone. Also when i replaced the heatsink, it was not seated properly and it shook when tested. upon fixing all these problems the computer started up and IS working fine. THANKS SO MUCH AGAIN.

You're welcome, glad you got it solved.