Have you checked the settings on the iPad? (go to the Settings, and tap "Video" on the left)
It has options for TV Out.
Also, check to see if there are any settings in your Pioneer TV Menu for configuring the input you're using. I've got an older Pioneer Elite 610HD that does only 1080i also. The TV menu has tons of settings.
Oh, you an also try doing a cold reboot of your iPad with the cable plugged in and the TV on. Do the "hold the menu/power buttons, and slide-to-power-off" thing, not just hitting the power button. That's kind of a long shot, but it's worth a try.
I have the VGA cable for mine, and it works with both my TV's, but VGA generally doesn't give people much problems (as it's a straight Analog signal.)
I have an Apple TV 2, and honestly, it's a much better experience. Almost everything supports AirPlay now. (CrunchyRoll.com is the only site I use that gives me problems, it supports audio only on AirPlay which is a bummer.)
Good luck! Let us know if you get it working.