Computer starts then turns off.

So here's the problem. My friend decided to move my computer while it was still on, at which point he dropped it and it turned off. I opened it, and the heatsink had popped loose. I set it back on correctly, started it, and it turned off within about 10 seconds. It doesn't usually do it at exactly the same place, sometimes I can even get into bios for a couple seconds. My guess is either the processor and/or the motherboard got damaged. I'd like some opinions on how best to proceed. I'd hate to buy a processor to find out it was the motherboard instead.