I had a situation exactly as you describe. The problem for me was that the charging pin had a poor connection with the main board. If you compare the plugs of your various micro-usb leads, you'll see that the female aspect can vary a little in height between them which I guess is why it works for some cables and not others.

My solution was to go to the cell phone market and have the repair guys solder a new usb plug on the board for me.