My 04 Xfire (108k miles) is suffering from no start.
When the key gets to the on position I can hear some fans or solenoids sort of semi struggling. Then engaging key in start position starter doesn't engage, no click nothing.

I removed the RCM and took it to my electronics guy who resoldered 30 points on it including the big 3. Popped it back in still no start.

I tested the battery, it is outputting 12.43v and 749 cold cranking amps (higher than rated).

I replaced the fob batteries and reprogrammed it.
Works fine unlocking and locking 3 flashes.
I tried the computer reset (disconnecting neg battery and shorting for 15 minutes).

This is what is odd, after resetting the computer and reconnecting, I can get the car to start perfectly exactly once on the first try. However it dies after 2 seconds. Then it won't turn over again unless I reset the computer again.

Any ideas what next?