How to confirm if GPU, CPU or motherboard is broken?
It sounds like you may have shorted your GPU. Try probing any lines going to the chips, and seeing if they have any signal. Be sure to be careful when you are poking around and the computer is on. Also make sure that the chips have some type of heat sink if they need one.

Personally I do not know of anyway of repairing a broken gpu (aside from replacing the motherboard)

In my opinion, I would consider the laptop scrap, and salvage any interesting looking parts (I like the keyboards and mice). Please make sure to destroy the Hard drive if you chose to scrap it (a good game of Hard Drive baseball is always fun!)

As for figuring out the pinouts on the monitor; I would do some DEEP research into the model number. About 75% of the time you can find some sort of semi-useful datasheet on your laptop components. If you have any trouble with this, be sure to post the question here.