If the relay is activating for ~ 3seconds when you turn the key on, the ECU should be fine.
I woudl look at your wiring. It seems there may be an issue in getting power from the relay to the fuel pump. Te power to the fuel pump is also the power for your fuel injectors. Your ECU grounds the other side of your injectors to make them fire.
Pull an injector clip and attach the positive side of a volt meter on your injectors and the other side to ground. The wire you are looking for is Yellow with a red tracer I believe. All 4 injectors share this wire.
When the relay is active there should be +12v at these wires. The relay is active for teh ~3 second prime pules, and also when you are trying to crank and when the engine is running.
I would look to be sure there is power going to the relay and coming from the relay.
John
John