Normally I would say for you to just fiddle around with the HDMI cable a little (sometimes it's seems like it's seated correctly, but it's not).
Try a different HDMI port on your TV.
Power cycle your TV.

This problem usually means that the "handshake" process between the display and 360 isn't being completed. But the reason your case is weird is because this is strictly an HDMI process....it shouldn't even be an issue when using an analog (component) connection.
Does the signal go through a receiver or HDMI switch before going to the TV?