Did you try cleaning the cartridge contacts? Or try opening it up and see if there's something broken or loose inside?
What model GG is it? Does it have the grey dots printed next to the screen, or are they color? (IIRC the TV tuner only works right on the color-dots model)
It's probably the tuner, if you got it as one bundle. Start with cleaning the cart contacts, and see where it goes from there.
Like bic said, IIRC only the Sega-manufactured ones will work with the tuner (colored dots). Later Sega allowed a company called Majesco to re-release it (grey dots) but it won't work with the tuner.