is to see if the TV menu comes up. If it does not, you have some sort of electrical problem with the TV set. If it does, you need to change it off of CATV to something else so that the rabbit ears can work with it.
Strange that you have sound and no picture. Maybe the tuner is broken? It tells me that you are using the right input jacks for audio, but for some reason the video is not coming up.
Do you have the digital to analog converter for the DVD player? If using coaxal cable, try plugging it directly to the TV and bypass the DTA box. I am betting that the Cable TV box is still connected and somehow messing with the video signals. You may need to power off the Cable TV box or remove it. Power off all devices and attach the rabbit ears. Any one of them could put up a black screen. My wife often leaves the VCR on and my son changes the channel to something other than 3 and it shows a black or blue screen instead of snow. Same deal with the DVD player, only it goes into some sort of screen saver mode with no action or DVD in the drive and shows a black screen.
Got another TV set you can drag to there to try the connections out with? Small portable? If it works, suspect something is wrong with the big TV set.