The component connection (red green blue coloured RCA's on the back) certainly does output all the resolutions including HD. Are you sure you haven't accidentally connected it to the composite (yellow white red RCA)?
Failing that, go to settings, video output and make sure its set to the right resolution. Or use the button on the front of the Tivo to cycle resolutions. Sometimes after a reboot mine was defaulting back to 576p and I had to manually change it, maybe that's what happened?
Possibly there could be a limitation that the Tivo won't simultaneously output HD on both HDMI and component, as it sounds like you are trying to use both?
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