Blu-ray HDTV Conflict

I have an old Sony 55-inch LCD rear projection TV with one HDMI input (Model# KDF-E55A20) in my family room. I purchased a Sony Blu-ray DVD player (Model# BDP-S300) not long ago. The TV works fine with a Comcast HDTV/DVR box through the HDMI, but when I switch to the Blu-ray player it will not show a picture. I have the player set to Auto to acquire the correct HDTV picture (720p is the max for this set). The Blu-ray works fine on my new Pioneer plasma TV upstairs.

Two questions - (1) Have I been screwed by Sony (backwards compatibility) or should these work together? (2) Can I use a HDMI switch box that would allow me to hook both the Comcast box and Blu-ray up to the TV? Would a switch solve the compatibility problem?

Thanks!