That looks like it's a logic board issue. You could try taking the logic board out and heating it in an oven (or with a heat gun) for a few minutes to resolder the broken connections, but there's no guarantee that that will work. The computer is so old that it's probably not worth it to repair if the reheating doesn't work. Apple will want something like $1200 for a new logic board and, although they can be had for less at other places if you look, the computer's already so old that it really isn't worth it to fix it.
Sucks, I know. My friend's MBP crapped out like that and it was too costly to repair. Luckily for me, though I have (and still use) the same model I haven't had the same issues. He gave the broken computer to me and I have something that I can use to scavenge extra parts off of if I need them.