Hey, I'll say that I have no problems, but that doesn't help.
What TV do you have the 360 plugged into?
I assume you're using the bundled in 360 Component A/V connector (as that's the one with the switch)

I'm guessing that your tv does not show 480p via component in.  Look at the specs of your tv. 
My bet is that it's not a 360 issue, but your tv.
Maybe you can change to the 360 VGA connector if your tv has that input.  It's likely that your TV will support more resolutions and refresh rates on VGA than on component
(I know of some projectors that will not do 480i or p on component.)

good luck,
 'Fish