On My Xbox 360, When I Switch to 1080p, the Screen Just Goes Black. How Do I Fix This?

We just got a new tv a few days ago, a Panasonic/Viera 42" 1080p LCD HDTV. It's using the component and HD cables, all plugged in correctly, and the switch on the cables is set to HD. 480, 720, and 1080i all work fine, just not 1080p. The screen just goes black. Any suggestions?

Suggestion:

Maybe the TV doesn't support the resolution even though it maybe labeled as 1080p. If you supply the model number for us we could do more research and troubleshooting. Have you tried the HDMI cords yet, they run at about $6 that includes shipping too.