Although the pump is priming, it sounds as though it doesn't run in the no2 position.
You've pretty much established this with the easy start, connect the pump up direct to the battery, or use a jump pack etc, then try it will no doubt start perfectly.
In which case easiest thing to do is wire direct from position 2 on the iggy switch to the pump but MUST go through the fuel cut off switch, maybe this was bypassed as was faulty in the past ?
The ecu normally outputs a earth to the fuel pump relay, the circuit for which seems to be intact as it primes, so would seem a duff ecu.
tabetha