Finding a short on surface traces would be a good thing because you can just start pulling chips until the short clears. What I was referring to is if there's a short to ground in one of the inner layers of the PCB, you'll have to do more intricate surgery to remove any IC legs using the offending trace(s) and route the lines externally on the board, which can be a nightmare.
But to do this sort of stuff, you'd really need a logic analyzer and a bench power supply so you could inject power to specific parts of the board. If you find a part with excessive current draw or that gets really hot then you've found a problem.