Last winter we had an '06 or so Tundra towed in for a no crank, no start after sitting for 3 months. The engine bay wire harness was chewed up so bad that there was no repairing it. A new complete harness was something like $4400 plus something like 10 hours to replace. We found a used harness from a salvage yard for $1000. Installed it and still no start, the ECM was dead. All I can figure is trying to crank it with dozens of wires shorted fried some circuitry inside. Another $1400 and the truck finally ran.
Rodents in cars can be a pretty costly affair. Original Poster should be glad the bill was only $600.