Connecting to network printer

My friend got a new computer and is trying, unsuccessfully, to connect to a network printer that he says he has used in the past, in his one man office. He gets his internet access through a wireless router. But the printer is connected via Ethernet cable to a second router that does not have internet access, but does have two printers connected to it.

So his new computer is connected to two different networks, the wireless network, and the wired network. I'm not familiar with having your computer connected to two networks simultaneously.

So my question is, is there any problem doing it like this, and should the network printers show up when the computer does a search in Add Printer?
Because it does not find anything right now, not sure if we need to be looking at the printers, the router, or the computer.

He is not able to connect the printers to the wireless router, they are in different rooms. And there are no other computers connected to either network right now.

Thanks

OK I was able to fix this by rebooting one of the routers.