You will fry your cpu if it does not have a heat sink properly installed.

The good thing is that AMD cpu boards are usually a bit cheeper than intel cpu boards. There are really only 2 AM3 boards that are SLI. So your not going to have any problem with finding the board you want in a amd/ati graphic.

You could try a new cooler. They usually have adaptors/brackets to fit different boards. So if your old board still does not work right with a new cooler bolted on, you could still use it for your new build. Still strange that it does not work if heat sink is clamped on. Something is loose.

Good luck.