Why is my MacBook Pro intermintant?

It seems like my MacBook Pro A1150 is going into some kind of over heat mode. About a minute or two after booting the screen just goes dark and the fan start blowing at max.

I think this is some kind of power or heat related problem. Resetting the SMC helps greatly and sometimes it can make it all the way through booting, I have even been able to format and reinstall OSX without crashing, but eventually the same symptom returns. Also I can almost always boot it in safe mode with no problems.

I took it in to the apple store and they said the logic board was shot and needed replacement, but I'm not buying it. Could this be a bad temp sensor or mag safe board? I have already disassembled to replaced the thermal paste and checked to make sure the temp sensors are in place.

Also the person who owned it before me managed to destroy the transformer in her AC adapter. Not sure how or what damage that might have caused to the laptop.

Any info or advice would be helpful, Thanks.