Your laptop uses the printer's native language, not AirPrint that the iPad uses.
Your new WiFi router may not correctly handle Bonjour data that AirPrint requires. If you contact the router's manufacturer, there may be a change to its setup or a firmware update that will fix the problem.
I was not clear. The router is not new. It is the same one we've been using. The router is not connected to the Internet. We are just using it for intranet.
I think the bottom line question is does the network have to be connected to the Internet to print? All three iPads and three laptops are all on the same network but it is not connected to the Internet. The laptops can print the iPads and my iPhone cannot. When the router was connected to our cable modem and was therefore on the Internet the iPad/iPhone could print.