Repairing a Rock Band guitar's tilt sensor

Last week, I decided to play Rock Band. If you don't know anything about this game, you might just want to stop reading now. If you have played the game, you are probably aware that in order for a guitar/bass player to activate the "overdrive" feature, he must either tilt the guitar into a vertical orientation or press its start button. Although some players disagree, I find that it is far easier to tilt the guitar than to press the button.

Well, since the last time I played, the tilt sensor in the guitar broke. No matter how much I tilted the guitar, the overdrive mode would not activate.