What does your last line mean?
Could it be my older TV can't put out enough signal for the new box?
Your cable box should be plugged into the F connector at the wall which goes out to the cable feed for your home.
If your cable box has component (red/green/blue) connectors, then I would connect them straight to the TV.
If that did NOT work, then I would plug the yellow (composite) conector to the TV and see if I got a picture that way.
Your TV may only accept certain signals on the component video input, such as 1080i. If that is the case, then you need to set your video output from the cable box to 'FIXED' and to '1080i'. This may solve your issue, but you will need to go all the way down to composite, or even 'RF' perhaps to get the video on screen to make this adjustment.
Once you are set to 1080i fixed video output, then I would go back to a direct component video connection, then back to the receiver.