There is one pin on one of the computer plugs which primes the fuel pump when you first turn the key on. My car leaks water sometimes, water got into the plug and corroded the connection and the pump wouldn't prime.
Replacing the computer may not be necessary since unpluging and reconnecting the plug cleans off the corrosion just enough to get the relay to kick on. I did the computer swap then put my old one back in and it worked OK, thats when I noticed the prime pin problem.
Spray the connector and computer pins with contact cleaner, blow it out and put on a small amount of dielectric grease. This took care of my no start problem.