You have 2 choices IMO since you used YOUR component cables with the test on your freinds display and have ruled out the cables and the 360 as the source of the issue. It is highly likely that it is oyur display that is the problem, but it COULD be the cables are too close to the power cables for some devices. I suggested you move the component cables away but did not see if you tried this. You SHOULD try this as it costs nothing but a couple of minutes max with no cash outlay.
If that doesn't solve the problem, then it is the component inputs on the display and you need to either bite the bullet and bring it to the store to exchange it, or have Panasonic send a tech to fix it under warranty.
YOU have to make that decision, but i would exchange it myself.
Good luck!