It's not fake. This actually happens frequently with cartridges...
If you bought it used, then, it's probably just that the eternal battery has died, and you'll have to replace it. There's already a thread on here that explains how to do so.
However, I don't know. If you bought it used, and the cartridge isn't silver and sparkling, and just looks dumb, then, maybe it is fake... But, I think it's more likely that the eternal battery just died.