I was on my Droid X and it had about 75% of battery life left and it just randomly shut off. I plugged it in and it shows a green light and doesn't turn on. I removed the battery several times and what not.
If you have a solution let me know!
I have had several problems with my Droid X turning on and off. Recently I found out that it must have gotten wet when I dropped it. Check if yours is wet. If it is, try putting the battery and/or the phone into a bowl of rice (Rice has been know to extract excess water, as well as bread has.) If it is not wet, I would say take the battery out for a couple hours, try again, and if even that doesn't work, take it to a Verizon store or premium retailer and see if they can help with the problem.