Greg has a DVD/VCR combo, but it only plays in black and white. Leo says that the likely culprit is a bad composite cable (red, white, yellow). So he should replace that. They're pretty cheap. ScooterX in the chatroom says that in the memo of the DVD player, there's a setting that could be affecting it. The TV may be using the same jacks for component as it does for composite. He should check his menu settings. TomsGuide has information on how to do that.
Joey inherited an LCD TV and he needs an adapter to plug in from his old coax cable box. Leo says that coax is an analog connector designed largely for over the air antennas, rather than digital, which is what HDMI or DVI is. Leo says it's going to cost Joey more to get a Coax to DVI converter than it would just to get a new cable box. Then he can get an inexpensive HDMI to DVI adapter. He'll also need a separate sound cable. Since Joey also has component, another option is to go from Component to DVI. That's an inexpensive option as well. But then he could end up with sync issues.
How can Robert move from component to HDMI? Leo says that component is the last bastion of analog and he'll need a digitizing box to move to the digital signal of HDMI. But that's only half the problem. Robert may have an issue with copy protection as well with HDCP. There could also be sync issues.