This happens to me as well. If I had known the Droid 2's battery life was this bad I would have opted for another phone. Anyway, what I've found is that if the battery goes under 15% and shuts off, charging it by the usb port on your computer takes a long time. However, if you use a usb wall charger it should start right up to the Motorola splash screen but it will go into charge mode where you will only see the battery and the percent of charge. It will not actually power up until it gets to about 25-35%. So you'll have to wait.
I've owned my Motorola Droid since about April. I love the phone, although the battery life is completely awful. But anyways,
I've been using a phone charger from an env2 to charge my droid (i lost my stock charger). The env2 charger is old, and was worn down a lot. Last night when I was charging my droid, I took the charger out and the charger head stayed in the phone, while the wires came out of it. So, I figured this morning I would go buy a new charger. So I come home with my new charger, and plug it into my completely dead phone, and it WILL NOT TURN ON. The white charger light is on, and its been charging for about 2 hours, but the phone will NOT power on. PLEASE HELP!