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Mine dropped below 5% and turned off. Plugging into computer still would not come on, but plugging in the wall charger brought it back.
) rooted it yesterday.

So I had the same problem in my car with the car charger. Funny as hell. 1981 911SC Targa. Never had a charge problem... But I never tried charging at night. Turns out the gauge lights and cigarette lighter are on the same circuit. Never had the lights on in the day. The gauge lightd pull enough
power to drop the charger level down and kill it. I am hard wiring a 7805 +5 volt regulator chip to a separate fuse. It will put out 1 amp+ 1000 miliamps. No more BS. The 7805 is so cheap I don't know why they didn'y use it in the charger to begin with. I'm going to rig a 9v battery on one for emergencies.
New and strange problem today with my Droid. I had it plugged into a charger all night. This morning as I am working I hear the 'Droiiid' sound. I go to see what came in and my phone is off. On the charger. The white light is on. I try to turn it on and it won't. I pull the battery and it still won't turn back on. Nothing I do seems to get it to turn back on anymore. I can't even use the x+power start up.
Any ideas?
I'm going through this no boot, battery life issue right now. Mine all started when I allowed the battery to fall into the orange zone. I never received any warning about being low. I plugged it in immediately, but the phone shut down on it's own anyway. I struggled with battery pulls and restarts for quite some time. Left it to charge on the Motorola logo overnight.
The next morning it started just fine, but the home and search buttons didn't work, and holding the power button showed only Power Off, and no airplane or silent modes. I used it like this for about 2 days.
Today I could not get it past the logo no matter what I tried. So I went to Verizon. He got it to start using the cable but no battery. He assumed it was the battery, so put a new one in. But then couldn't get it to start at all.
He didn't know what it was, so now I'm getting a new phone, and I get to keep the new battery. The new phone may come with a new SD card too, if not, I can go back to the store and get a new one. He kept the old battery.
Lucky for me, I had just performed a full online backup (apps and data). My phone is NOT rooted.