The name of this site is iFIXIT so If this would happened to me I would open the laptop by going to a video on laptop disassembly with my model. (antistatic procedures taken) I would place parts under the sun on a sunny day or use a heat blower and blow on the motherboard at a certain distance using my judgement. I would ensure I use a anti-static wrist band when emsenbling all parts back together. I would clean the board before everything is done by spraying isopropyl alcohol and brushing with a tooth brush. I would REMEMBER to put apart the HDD and the CPU. I WILL NEED thermal paste afterwards to put some on top of the CPU when placing it back into the socket.
I might solved the problem by taking the RAM sticks out of their sockets and cleaning the contacts with an eraser. I use Lion Deluxe. I would put them back and turn on the computer. I might be lucky with this.
If neither of these works them it get complicated because a Digital Power Supply and a multimeter, etc. is needed. Probably with only a multimeter I might solve the problem in finding that shortcircuit but know-how is needed to do that and understand electronics and how to troubleshoot Mosfets, etc. This is only my opinion. This last method required equipment, expertise and experience. This is called chip level repair. Good Luck!