[Cajundaddy]

Process of elimination...
I would change the ign. switch first because it is cheap, easy, and a likely suspect. The DME and immobilizer are a can-o-worms because they are tied to the car and key. Swapping them out is no simple task. You can disconnect/reconnect them or open them up to inspect for damage. Rodent damage to the harness is also a possibility especially where it passes through a bulkhead or firewall. Good luck!