I recently changed my setup for the above from component video to HDMI. My previous connection was Component TIVO -> 350 -> TV. Everything worked fine, including the remote. Now I have the TIVO connected to my TV via HDMI, and the Component TIVO connected to 350. So the connections are:
HDMI Tivo -> TV
Component Tivo -> 350
With the above connection I can see and hear the channel, but the remote doesn't work.
As you were using component cables to the 350 in both configurations, simply removing the cables from the 350 component OUT plugs should have had absolutely no effect.
and come back if it doesn't help,