Here are a few people talking about something that you absolutely need to check:
http://www.ls1gto.com/forums/showthread.php?t=377773
(Note: This might or might not have been my problem below.*)
My car was going bonkers the past few days, out of nowhere. It started last Monday. I went to turn my car on, and
everything turned off. Backed the key out, and tried again... same thing. So... I checked something out. I turned the key to see if the electronics would turn on: Nope. The CEL was just flickering like hell. After 2 or 3 tries, the time on the radio reset. So... I automatically thought it was a battery issue. I ended up getting my Dad's voltmeter, and the battery was reading 12.6 V. After a few tries, the car finally fired up. Went about my day, and it didn't do it for a few days.
Thursday morning, same thing. Crap... I thought I was gonna be late for work. It only took a couple of turns to get the car on this time. Worked good for a couple of days this time.
Yesterday (Saturday), I was gonna go visit my Mom in the hospital, and same thing... car wouldn't turn on. This time, it would NOT fire up. I turned the key to see about the electronics again, and it was that constant flickering again. I followed the sound of it, and it was coming from the fuse box under the hood. Once I took the key out, the sound went away. After I ran all my errands, I started looking throughout all of the GTO forums, and found the resolution above.
Today (Sunday), the first thing I tackled was the BCM Harness. Got under the glove box first, and could see a little wear in the cloth. Took off the glove box no problem, and didn't even break the clip.

Put some electrical tape around the wires/cloth, and put a little tape across that metal edge. I need to find some foam tape, though. I don't trust the electrical tape on that edge.
Now... in addition to the BCM check above, I did a little "fix" on the positive connection on my battery. I can't find the thread again, but good ol' Kingsize mentioned something about that plastic on the bottom of the Positive post. According to him, that little piece sometimes messes with the positive connection, so he says to just remove it altogether. I did that, and voila! Selena fired up perfectly.
*So... I can't tell you if my problem was because of the BCM harness, or the positive connection, but this is something you should all check. If I can do it, then most of you should have no problem doing it. This is only a few hours after the fix, so I'm hoping it doesn't come back. I'll update if anything changes.
I have a video of what the problem looks like, but it's on my crummy cell phone. Not sure if I can email it to myself or not.