Try a different charger. Are you using the power supply that came with the unit? I own one of the original Tabs, and it requires a high-current power supply (about 2A, compared to the usual 550mA). Anything less, and your battery won't charge.
On top of that, I have also experienced this with a good power supply, and a defective USB cable.
Bottom line: Go someplace where you can try another power supply/cable, preferably one out of another package. If it works, that's your problem.
The GTab's seem to be way too picky, when it comes to power needs.
