Okay, just remember your Cable box must connect to the DTV component inputs on your TV set, because that input is actually 1080i and the ones NOT labled as DTV are only 480i/p input jacks.
DVD players do 480 with the component outputs, so they will work on ALL of the component inputs, including the DTV input.
Back when your TV was built by the manufacturer, they only put one HD Component connection on TV sets, and Mitsubishi labled the HD jack as DTV.
Today's cable boxes are all 1080/720 output, so they must use the DTV jack
But, you do want to use the HDMI input I'm sure. The problem with that is CABLE boxes just don't work reliably with it, especially if the Cable box is the MOTOROLA brand.
I've seen some Scientific Atlanta boxes do the same thing, so I have been telling customers to use the Component inputs for the cable box and use the HDMI for the Blu Ray players as they are more reliable with it.
There was also a series of Mitsubishi TV sets, where the DTV component inputs could be switched from YPbPr signal to an RGB computer-based signal too....if it was set for RGB you had a crummy picture with no sync, or it was green picture. If that's what you get with the Component connection, let me know that ok?
It was the hardest thing to find in their menu, but it could be on your TV set, as it's pretty close to the time they were doing that.
Now, the whole point about the EDID is the fact that the TV was built years ago, and the newer boxes have newer EDIDs and it may be the cause of your problem too....New equipment on older TV sets may just have to use the COMPONENT input as a backup input in your situation.
In fact, LG just created a brand new TV set that if you have HDMI problems, the service tech can actually go into the service menu, erase the OLD EDID and have it Re-Learn it !
I just saw one a couple weeks ago. Now that's SMART of them.
But nobody else has it yet.....