Doesn't do it when you plug it into a USB, but does it when you plug it into a charger. Is that correct? And are you using the Motorola charger that came with the phone?
Same thing happened to me but the other way around. I plug mine into my pc and it restarts. Its a matter of one battery pull. That solved my problem. Hasnt occured to me since i did the battery pull.
I've done a battery pull since 340 came out and my DX will still do this. If I turn it off and then plug it in to the charger, it USED TO just turn the screen on with the battery status showing but not a full boot up. Now it will indeed fully boot up. I have to turn it off again (this is usually done when going to bed) or plug it in then turn off.
Theoretically, I shouldn't have to turn it off at all, of course. I just do some nights.