Had exactly the same issue, I left mine plugged 24 hours to PC to charge to no avail. Had to open it up and check the voltage of the battery which was low 3.4Volts instead of 3.7. I am afraid the solution is to replace the battery. Once the voltage increased to over 3.5 the unit came back to life for a while, although the battery was not up to maintaining the unit powered up, but long enough to re-assure myself that my files were all there. If you Google it there are instructions of how to open up the unit. Not sure yet where to buy replacement battery but again there may be some on the internet for sale.
Hope of use
Andy
May 2009