I experienced this today! It was so weird. I was texting, and the battery was around 10%, so the 15% battery warning came on. I went to plug my phone in, and the battery warning went away, BUT the battery icon wasn't ... "charging," and nor was the white light on. I unplugged it, and the warning reappeared... plugged it in, and it disappeared; battery icon was still the same. So, my phone eventually died *tear tear* and I'm just... perplexed as to what the heck happened! It wouldn't turn on, anything. Though it went into the bootloader for a few seconds, and I also got it to enter recovery (CWM) mode for a sec, attempted a reboot from there, and it died in the process... xD
I just let it charge (wall charge) for about 2 hours and it eventually turned on. It was around 6:30 when it finally died, and just a few minutes ago it turned on. I'm guessing, as it turns out, it was too dead to charge before... but I don't get how it didn't charge when it was still on! Weird!
edit - ... it died. 5 minutes later, the phone is now.. cold. its quite obvious that it is NOT charging... any suggestions, besides the obvious get a new charger/go to Verizon?
edit#2 - okay, so i had the supplied USB cable plugged into a USB extender cable which plugged into the wall adapter. apparently, that was the culprit of my situation. i omitted it, and my phone is charging fine.