Alright guys, i'm going to do my best to document everything i've done so far.
I got my phone, and within the first 24 hours, I would lock the phone, and everything would lock properly. Then, I would press the unlock button, only to have the backlight come on for the bottom 4 buttons (Back/Menu/Home/Search). I would press it one more time to turn it off, then again and it would turn on properly. Since I didn't know otherwise, I considered this a "feature". Another minor problem was that the screen would not turn back on after I was in a phone call unless I was in direct sunlight. I would have to unlock the phone, which was already a problem of its own.
Over the next 24 hours, I would have to press the unlock button more than 3 times, sometimes 12-15 before it would come back on. I intuitively pulled the battery, and, it began to work.
Within 30 minutes or so, it began to happen again. When I called Verizon, they instructed me to pull the battery. Of course it worked, but when I told them that I had done that already, they said,"Well, this is your first documented time calling our technical support. If the problem continues, please call back." I took offense, but carried on.
When I did another battery pull, the phone wouldn't turn on. I was outside and couldn't tell if the backlight was turning on. 6 or so hours later, when I walked into my house and it was dark -- I noticed the backlight had been on the whole time. The phone had not booted, though. I also tried the "hard reset", but that wouldn't work -- as it would not boot.
The few apps that I installed were ShapeWriter and AndChat. That was it.
I'm going to write this whole thing off as a faulty device, and taking it back to Verizon for a new one today.