psc 1350 and network?

OK, next step - you need to change the IP address of the print server to be in the same subnet as the computer and router. Look at the IP address of your computer and change the last part for the printer to be away from the computer (example - computer 192.168.1.3 - printer 192.168.1.200).
You could do that using the OS 9/Classic app HP Laserjet Utility (free download comes with OS 9 laserjet drivers - even though you don't need the driver). Or, you can use the Terminal (Utility):
telnet 192.0.0.192

If the PSC1350 is a major change from the 1310, maybe it won't work because there is no driver -- but I seriously doubt it.

Yes, you need to use cups drivers:
http://www.linuxprinting.org/macosx/hpijs/

The Deskjet 900, Gimp-Print driver already on Panther may also work for that model.

The MAC address is never used in any Printer Setup.

You didn't say which router you are using. How are computers getting their IP addresses? Are they in the same subnet? You should use the IP printing/HP Jetdirect protocol with no queue name entered.

You should try to add the printer (1350) using the IP > HP Jetdirect protocol, and the hpijs 1310 driver. The hpijs driver requires ESP ghostscript from the same web page.

HP will not say anything about network use, because their driver is intentionally limited to USB use on OS X.

When you say the Socket/HP Jetdirect protocol, that is what it is called in the Advanced protocols. But, if you use the Advanced protocol, you have to completely fill in the URI like this:
socket://[IP address]:9100
But if you use the regular Tiger IP printer > HP Jetdirect choice (not Advanced), you only enter the IP address, because OS X fills in the :9100.

Does that help?