Well I'm sure that everyone has moved on from since the original post, but as I have just had a similar problem I thought I'd join the site and share what has worked for me.
I have a Go720 which I've had for over 5 years in full working order, however, I hadn't really used it for the last year or so. About 6 months ago I got it out to give it a charge and everything was fine. The I decided to do the same again last week, but this time I had no green charging light. There was still some charge in the battery so I knew the unit was still functional. Well 5 years for the battery wasn't bad at all, so maybe I treat the unit to a new battery. 8 quid, delivered, from fleabay and the new battery arrives. A quick search for a removal tutorial finds a really simple video showing how's it's done in around 5 minutes.
So, new battery in and all powered up great. However, I plug the USB cable in again and nada, still no green light. Another search for "no green light" just points me in the battery problem arena again. Then I think about various laptops I've had in the past where the soldering to the power input socket cracks and knackers the connection. So with the USB connected at both ends I gently move the mini USB end left, right, up then down and hey presto when I move it upwards the green charging light comes on. I apply just a little more pressure to the upwards movement and there's a gentle click inside the device, almost like something popping back into place. As I type right now I have the unit beside me charging unassisted. What a result! So I now essentially have a new device again, well chuffed and only 8 quid lighter.