Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question.
Check the firewall settings on the new computer - does it block the IP address the printer is installed at and configured to?
Is the printer configured to a fixed IP or static IP address on your local network? or does it get assigned a new IP address whenever the local router box is restarted?
Does the printer work with any other computer, or have you no other computer to test it with?
What MAC OS X version is on the computer?