Allright, let's try to fix this one.

  It started with our battery not keeping a charge.  We bought a new battery, and had the alternator checked.  The alternator checked out fine, but the new battery was still dying.  So my brother in-law replaced the distributor and coil.  He said they were draining the battery.  The car ran for three days, then my wife thought she ran out of gas.  So I brought her a gas can where she was broke down, but the car still didn't start.  We towed it home and this is what I've checked so far.

Note: Now, When I try to start the car, it turns over and will eventually start but dies instantly after starting.  It takes a lot of turning over for it to start for that one second, but after it starts and dies it seems to repeat the cycle (amount of time it takes) to start and die again.

When we first got it home, when I'd crank it, it would crank,crank,crank, then poof, a weird poof sound.  It doesn't do that any more.

This is what I've done. 
I've replaced the spark plugs, still no start.  I checked the codes and there were none at first, then a code 16, so I researched that, and came to a conclusion that from constantly cranking the car over trying to start it I melted the solder on main relay.  So I resoldered it, Still no start.  I pulled the fuel line off where it connects to the filter, turned the key on and got sprayed.  I just got done checking for spark by holding a plug connected to a wire to the block, got spark on all four. 

After cranking and cranking I take the plugs off and they appear wet, only one doesn't, but why would they be wet if they're sparking?

So, I hope you can help, my wife's on her way back from the store with a voltmeter and alligator clips.
I thought that maybe my brother in-law messed something up, but it ran for three days after he changed the distributor and coil.  Do you see any connections?  In the mean time I'm going to check the ignition coil with the  voltmeter, and plug wires (though if I'm getting spark the wires should be fine, right?).  And my buddy said if I take the distributor cap off and I crank the engine, that the rotor should turn at a steady pace, and that if it  jumps fast and then slow or is irregular than I need to replace my timing belt.

Thank you guys and looking forward to your advice, don't know how much longer my Grand Am is gonna hold up for us