My son would like to play Angry Birds on out new 50" HDTV, so I asked the Apple store if there was an adapter to connect the 30 pin connector to my TV's HDMI to do this. They suggested the Apple digital AV Adapter, which I bought. Brought it home, connected it and nothing...no output whatsoever. Tried different HDMI cables in different HDMI inputs. Called Apple store back. One store says the Touch isn't supported (it lists the iPod Touch 4G on the front of the package). Called another store, who suggested Updating the iPod to the newest OS. Did that, still nothing. Called Apple store
again (not paying Apple Support to tell me it's just not supported device), now they say I need to spend $100 on Apple TV and go through Airplay. If my "smart TV" didn't already give me Netflix, Hulu, etc., I might consider splurging on an Apple TV. But is seems pretty frivolous just to play a couple games

Outside of jailbreaking my iPod, is there a way to mirror a Touch 4G through my HDMI input?
Thanks!