Multiple video inputs
Unfortunately, you cannot use the connectors at the same time. The S-Video connector overrides the standard video connector. This is why they share common audio left/right inputs. If you could use them separately, they would each have their own set of audio inputs. (S-Video does not carry audio signals on the cable.)
I'm assuming that you are connecting your Satellite as an input to your VCR, and then your VCR to the TV via a video connection. The VCR passes the satellite signal through unless you are watching a tape, then it overrides the dish signal.
You have a few choices here:
1. You can connect the coaxial (RF) output from the VCR to the TV, and watch the satellite and VCR on channel 3 (or 4). You can then connect the DVD via S-Video, and watch it on "video". This is the simplest solution, and provides the best picture quality for the DVD (with this TV), but lower quality for the dish and VCR.
2. You can connect the DVD player via RF (if it supports that), watch the DVD on channel 3, and connect the VCR via video. This will make the DVD picture quality terrible.
3. You can replace the VCR with a combo DVD/VCR unit. You can then connect the S-Video out from the combo unit to the TV. This is a more expensive solution.
4. You can replace the TV with a model that includes more inputs. This is the most expensive solution, but will allow you to watch your DVD over component cables (very high quality) and VCR and dish over S-Video.
Ironically, the obvious choice, connecting the DVD as an input to the VCR (as a pass-through) simply WON'T WORK. The signal put out by the DVD player is "copy protected" (using a system called MacroVision) which the VCR will refuse to play, even as a pass-though.
Best of luck with this. Given that you are trying to make this all work without replacing equipment, I recommend option #1, until you decide to break down and buy a shiny new HDTV. They are coming down in price every week, but only you can decide when the time is right.