However, the fuel pump works just fine with my regular chipped P28.

When I plug in my refurbished ECU with the demon, the fuel pump doesn't prime
and the car doesn't crank.

Could it be the ECU that I received or something was soldered wrong?

 

Does the CE light stay on? Try leaving the key in ACC and go have a coffee. If when you return the CE light is off and you can start the car, it's the ECU - I repair this issue daily.

 

The car should still crank without an ecu installed. If you mean crank as in the starter turning the motor over that is. If it is just the fuel pump issue then it's a pretty easy fix.

 

The CE light doesn't come on at all.

 

It's not a fuel pump issue. The fuel pump primes fine with my chipped p28. It's just this ecu with the neptune demon installed that doesn't prime or crank (motor running).

 

I didn't mean the fuel pump itself. The ecu needs repaired if the pump doesn't prime, and it does with a different ecu.

 

It's almost definitely a bad ecu, this is not an uncommon failure on one that's old enough to buy you a drink. Good news is that it most likely can be repaired.

When the shop you got this "refurbished" ecu did the work on it, did they replace anything and test the the ecu or just clean the case and slap a sticker on it? I would start by contacting them, hopefully it's a minor mistake on their part.