Excellent suggestions from rglore and DVRexpander.
Following their suggestion, I checked the modulator ("Menu>system settings>installation>modulator setup" for those like me who did not know where to find such a thing) and confirmed for a second time that it was set to channel 3. I then went to the RF input for the TV, which was also set to channel 3 and still had fuzz, just as before. Since I did not realize that the output could be set to so many other channels, I went to channel 4 and then switched the TV to channel 4, out of curiosity. The TV fuzzed there for a while and then, as if by magic, a picture appeared. I then switched the modulator and the TV both back to channel 3 and the signal was now visible on that channel.
Having confirmed that the receiver was now sending a signal, I then hooked up the coax from the dish receiver to the analogue TV I was trying to get a signal on and there the image on that TV. Apparently, the DISH receiver needed some sort of confirmation, either from the modulator being set or from an exchange with the TV, that the modulator setting is, indeed, the correct one.
I may send a message to DISH technical support as they could not figure it out, after spending time making sure I had a signal input rather than telling me how to check the output. As a result, I received a second, apparently unnecessary replacement.
Thanks again for the suggestions.