So, here's exactly what happened, and what I've tried.
My phone was just fine, running perfectly, nice battery life. I had been running CarbonROM for about 2 months, without any issues, didn't change anything recent to this problem occurring. So one night I was at a party, and didn't have an available charger, so my phone ran out of power completely. The next morning when I came home, I set it to charge, the LED lit up, as far as I remember at least. In the evening I turned it on, and I got to the SIM pin-code unlock screen. I entered the PIN, and my phone turned off. No crash screen or anything, it just went straight out. I figured that maybe it hadn't charged properly, so I let it charge for a few more hours, and then tried again - same thing happened. I instantly tried to turn it on again, but this time nothing happened at all. I held the power button down for at least 1 minute, to no avail. When I put in the charging cable, the LED doesn't light up.
So, as I said, I have been reading around on this forum and other places, trying to find a solution. Some people said holding down the power button and volume up and down at the same time for 2 minutes would fix it, it didn't. I have tried several times. Most recently someone said I should connect my phone to my PC with the USB cable, and then hold down the power button and volume down. This time, something did happen. But not on my phone's end. I have done this 2 times, with the same result. At exactly 7 seconds, my computer turns off, as if I had "choked" it by holding down the power button on the PC. This seems really odd to me, since the phone can't even turn on, so I don't see how there can be any connectivity.
I hope someone here has a solution, knows why it happened, or can at least guide me in replacing any part if needs be. I hope not, though.