First of all check the ENGINE EARTH STRAP. I have seen that cause this same issue many times.
If not...
Run a cable direct from the battery to pin 20* of the ecu and try again. If it works, the fault probably lies in the power relay circuit so you can just rewire that part pal. If not, run one from chassis to pins 1 and 19 and try again. This is your earth circuit. If that fixes it, the solution is NOT to rewire direct to pins 1 and 19, so please ask for further information on this topic.
Good luck.
*
I am suffering from flu at the moment so PLEASE check that number is right for the positive feed. I'm sure it is but I'm dizzy and sick at moment.