Why isn't the iTrip working with my 4th Generation iPod?
The first thing you should try is updating your iPod, which fixes this problem most of the time. If you have iTunes 7, just click on your iPod in the left column under "Devices" and you will see an "Update" button on your iPod's summary page.
Run the updater, and after that, you can plug in the iTrip. Play a song and it should power up.