VicVarron

Ok, so back in April, I posted an issue with the car not wanting to start on damp days, or after it rains in this thread .
Since, the problem has pretty much gone away until now.
It started back when my son accidentally left his lights on all night and drained his battery. After jumping it and letting it idle for about 10 minutes, he went to leave for work. Car stalled and died when he put it in reverse.
Jumped it again, this time checking voltage to the battery. While hooked to cables, battery read 13.6 volts. Once I removed the cables, the battery went down to 12.4 volts.
I assumed the alternator was going bad since the voltage was dropping while the car was running. The battery was replaced in Feb of this year, so i didn't suspect it as being bad.
I replaced the alternator, got the battery charged, and he drove it fine again.
Then the failing to start issue came back. It acting like its out of gas.
I pulled the main relay and checked the solder joints and reflowed a few of them that looked questionable. I then pulled the fuse to the radio to try and hear the fuel pump (has an automatic antenna that was drowning out the sound of fuel pump, which is why i pulled the fuse).
I noticed the fuel pump is not turning off. Even after "fixing" the main relay. So, this morning I bought a new relay and replaced it. Fuel pump still won't turn off when the key is in the On position, and it floods and sputters when trying to crank.
I can now get it to crank pretty regularly if I don't let the fuel pump run for very long.
Does this sound like an ECU issue, or something else?