When I hook my cable box between my home theatre and HDTV, I get no picture. What can I do to use one input?
I have a Comcast HDTV box, feeding into my Sony Bravia home theatre system via coaxial cable, then to my HDTV via component cable. However I do not get a picture this way. I know I can connect the cable box and the home theatre system via separate component inputs, but is there a way to use both without switching inputs? Thank you!

You need to select the correct input source on your tv and the correct output on your theater unit. Yes, you can have multiple inputs to your tv, just be sure to select the input you want on the tv itself.
Yes you cannot do that. The only way you can do this is if you have an AV receiver. You still need to select the input on the AV receiver too.
Even if you COULD get this system to work, you wouldn’t want to. The coax cable output of the cable box will not be HD, it will be a standard SDTV signal. You want to connect the cable box to the TV using an HD compatible connection (either COMPONENT or HDMI).
If your TV has multiple COMPONENT connections, connect the cable and DVD separately. If the TV has a COMPONENT and an HDMI connection, use the HDMI from your cable (most HD cable boxes have an HDMI connection) and the COMPONENT connection from your DVD. You won’t need a switch, but you will need to use the TV’s “source select” feature to switch between TV and DVR.
Finally, if your TV has only one component input, go out and buy a component video switch (about $30 at radio shack).