Have you tried turning it off and on again?
Tech support joke.
First of all, your DVD/VCR will not record a digital signal. Your DVR can do that. So the fact that you cannot record to the VCR is not an indication that the VCR is not working, only that it's obsolete.
The rest of your problem is hard for me to give advice on, without actually being able to see your inputs/outputs/connections. Since you describe a red, white, and yellow cable, I'm assuming you do not have an HDTV? For regular old televisions, you should see on the back several slots coloured red, white, and yellow. Make sure the colour of the cable matches the colour of the slot. If they are connected properly, next check to see if the inputs are labeled. You should see something like "Input 1" or "Video 1." Let me know what all the labels are, as well as the colour of each slot.
Lastly, to you subscribe to Dish? That'll make it easier for me since I subscribe to them. DirecTV uses pretty similar equipment, though, so it shouldn't be too big of a deal. If you could let me know the model number of your DVR (for example, mine's a Dish VIP722), that'd also help. The model number should be right on the front of the DVR.