Is my motherboard shot?

The short answer: probably. It looks like some of the traces have been melted. I can't say I know what would have caused that to happen, but I'd say you have three options here: 1. Find out where each of those traces lead and solder in jumper wires to those locations, thus bypassing the damaged traces. 2. Replace the motherboard. You might just want to do this if you don't know how to solder. It would cost way more than the jumper wire method, but seeing as the N64 doesn't really have internal memory, it's a better option for an N64 than it would be if you were going to do the same thing with, say, a Wii. 3. Try a different output cable and cross your fingers that it works. I don't guarantee that this would work, but if your cable is faulty, obviously you won't get an image to appear. You might also consider making sure that you've actually got the outputs plugged in (if this turns out to be the problem, there's no shame in it- it happens to everyone). If you don't have an extra N64 cable lying around, you can also use a Super Nintendo cable or a GameCube (specifically the analog cables- the digital ones are really rare and don't even fit in the N64 output port) cable- they're all cross-compatible.