Honestly, I would not recommend putting the time in to fix this model, just resell it on eBay as is. For a start, the price of a new LCD and battery will set you back, and if you replace the screen, you might as well replace the hinges whilst open (these usually break on this model).
The main reason I would recommend against fixing this, is since this model is notorious for developing CPU, GPU and RAM (which is soldered on this) issues. Chances are, if you get this working, it will beep at you, or will develop this fault shortly after being sold.
I have a regular who buys broken MacBooks from eBay and sends them my way to repair. Last year, I told him I am not repairing these models anymore, since I would get them working to find a CPU/GPU/RAM issue, which was a waste of time, or he would get it returned from his customer within 2 months with this fault and have to refund them.
If for some reason you do decide to repair this, find the board number on the logic board and Google "820-XXXX schematics", which will give you some results. I would recommend taking my advice though :)