When your Droid 1 started rebooting while charging, did you happen to add any new apps to the phone.
First, place your Droid 1 in safe mode. Once it's in safe mode, plug it in again, is it still automatically rebooting again?
If it doesn't reboot that's a good thing because we know that an app isn't causing it to reboot.
If it does reboot while in safe mode, then there is an app on the phone that is causing it to behave in this manner.
If it reboots while in safe mode, you should remove the most recently added apps to see if that makes a difference.
As a last resort you can do the hard reset. Performing a hard reset will remove ALL data including the Google account, system data, application data, application settings, and downloaded applications..
You can save your contacts to the SD card by following these steps.
Please do follow up to let us know if your Droid works in safe mode or not before you end up doing the hard reset.
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Try as I might, I cannot get the phone into Safe Mode.
With the phone OFF, I...
The phone turned on...
But before I could press Wait or Force Close or Report, the home/lock screen appeared.