You said that the only port on the printer was a parallel? I'm not sure if they make them for parallel, but I I have a strong feeling you could get a print server and plug that into the router you mentioned. You could get a cheap PC and use it as an always-on printserver, or you could buy a network-ready printer with an ethernet port on it and a built in printserver. Not sure which would work the best for you, maybe just attach the printer to one of the computers, and leave it on 24/7 and just print to it. Only problem with that is that you have a computer running 24/7.
They make print servers for LPT device. If your printer requires bi-directions comm it will not work. HP sells print servers for their hardware but are expensive. But are guaranted to work if the printer is on their aproved list.
Their are routers that have print server ports on them. But only support 1 direction communication.
The only sure way is with a network printer. Recomend laser, because they are cheaper to operate.
I just stumbled on your forum while searching for a way to connect my parallel printer to my home network with using a pc and wanted to share this link with you. I think it is what you needed. Good luck!