i am having the same problem - right now - nothing.
This definitely sounds like a problem! I suggest removing the battery, cleaning the battery ports on the phone and battery with a clean cloth, re-assembling the phone, and retesting. If that doesn't work, I recommend filing an insurance claim (if you have insurance) here: http://bit.ly/07CrqPK Let us know the outcome of your situation!
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I'm having the same issue with my Droid X. If I turn my phone off for the night (charging or not), I have problems turning it back it. It may take anywhere from 20 minutes to 1 1/2 hours to get it to come back on. If I turn it off to charge it, I don't get anything. I've called VZWSupport twice and each time the people tell me that I've done something to the phone and make me think that I'm crazy. I'm glad to see that it's not just me having this problem. This is a TECHNICAL problem that too many people are experiencing.
I reviewed the device info to see if we had any updates on this trouble yet. I do see that Motorola has indicated that if this issues is continuously happening a factory reset will be needed. I recommend backing all your information up first to ensure that your important documents are stored. To complete the reset follow the steps on http://bit.ly/oV4Meh. Please keep us posted with the status of the device.
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the op's having a problem because the phone was dropped, not just powering on.