Where and to what was the printer plugged into before you moved? You mentioned plugging it into the modem and also plugging in your PC to the cable modem. Are these the same device and, if so, is what you have a modem/router combination? My first thought is that your printer doesn't work because it's in a different port and that port is not defined in your PC...that it's still trying to print through the old port. What has changed from then to now in that regard might be the cause of this issue.
I have an HP Officejet 6310 All-In-One Printer. Everything was working before I moved. When I moved and my internet was hooked up they told me I was wireless. My desktop does not have wireless so I did have to plug the cable modem to the computer. As you can see this works.
I have connected the blue ethernet cable from the printer to the back of the modem and it will not print. The printer shows ready when I go to the printer. It will not print a test page. I am not getting any type of error message.
Do you have any suggestions for me on what the problem could be? The printer is out of warranty and I'd really like to get working without contacting HP as they charge too much.