I had them same problem. I would add that when I attached the FLIP MinoHD to my computer via its USB jack, the led on the jack blinked continuously, yet the device was not even acknowledged by windows, nor would it power on after sufficient time for a complete charge.
Also, I tried the reset button hidden in the tripod socket, and called tech. serv. only to discover that repair would cost as much as a new unit!! Only worthwhile, perhaps, if you have very valuable video trapped in the device's memory. I didn't.
I looked at the disassembly instructions here at ifixit.com and determined that the first chip near the usb jack (TPD12S521DBTR) was a likely bad component and ordered a couple from digikey.com for $1.79 each. When the chips arrived, I opened my MinoHD only to discover it had a substantially different design from the ifixit.com version, and the chip I ordered was not in my design!!
I reassembled the dang thing, and it works fine. I can only conclude it was probably a bad connection or a bad logic state which was corrected by disconnection and reconnection of the internal components. At any rate, the video from 13 months ago was intact, and 18% battery charge remained. There was a frightening moment when first powered on where factory specs were displayed for minute or so, and an option to reset by holding the red button was offered. I tried that, but am unsure whether it actually reset. At any rate, videos from 13 months ago remained in memory and have now been safely off-loaded.
I have a few iphone pics of my unit's innards.