Instructions
Make sure that your game disc is properly inserted into your Xbox 360. The wireless "Guitar Hero 3" guitar-shaped controller will not work on your Xbox 360 unless the actual game is in your system and loaded up to the main menu. Insert your game disc, let it load and then try to use your Xbox 360 guitar again.
Verify that you are syncing your guitar controller to your console properly. To do this, with the game inserted into your console you must press down on the "Sync" buttons on both the guitar shaped controller and on the Xbox 360 console itself. This is similar to the way you sync a regular wireless controller to your Xbox 360. Even if your controller is on and the game is inserted, the controller isn't going to work if it doesn't know its supposed to be connected to your Xbox 360.
Stay no farther away from your Xbox 360 than 30 feet. The "Guitar Hero 3" wireless guitars for the Xbox 360 have a harder time staying connected to your system the farther away you move from it. If you leave the broadcasting range of the controller, this will disconnect the controller from your console. You will then have to sync the controller to your Xbox 360 again before you can continue to play your game.