Sounds like it could be an issue with the WiFi, since you are having difficulty finding any networks. WiFi cards which have gone bad can cause both an issue with finding networks and kernel panicking. It could be the GPU going bad instead, which can cause issues like this too, but the fact that WiFi is not working could indicate this is the cause.
First, try booting from another hard drive (external, by USB), to rule out the hard drive or software causing an issue. If the issue still occurs, I would order an Airport card and try that out, checking out the surrounding area on the logic board, to make sure nothing looks burnt or scorched. If you still have the same issue, try a new GPU, but it is probably not worth repairing in this case (expensive, difficult to find and will likely fail again, since pulled from a used unit).
I think it might be best on this occasion to try the Airport card, give the logic board a quick inspection, and if it still has the same issue, write it off unfortunately, due to the age, cost of repair and risk of the issue happening again.