Hey Kada
Firstly I doubt that you have done anything wrong. The only idea I have is that the IP address could have changed, due ot DHCP. How long has this setup been running. Do you know if the PCs are running on DHCP from the router, and is the full printer name on the problematic computer, (is it "Printer on <pcname>" or "Printer on 192.168.2.3". Which is most accurate?).
DHCP provides a new address after 3 days, and although in a small environment, this is less likely to change the allocation, it could be that the PCs no longer have the same IP, as when the printer was hooked up. Just get the IP of the PC with the printer, (make sure this hasn't changed, if you were taking it off a piece of paper, etc, for your ping), and on the other comp, Run
\\ipaddress
and see if the printer is in the list to conect to.
In order to check the PC's IP settings, type cmd in the Run box, then, use
ipconfig /all
Also, ipconfig /release and ipconfig /renew will (obviously) renew your IP settings.
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i pulled an ipconfig /release and renew on both computers, and checked out my router status page. in the DHCP clients list, it shows my second computer (192.168.1.101). I tried to navigate to \\192.168.1.101, and windows couldn't access it. In the command prompt I tried to ping 192.168.1.101, and nothing.
To answer your first question, on my computer it shows 'printer on [PCName]'.
I have no clue what in the world could have changed. Any help is appreciated
edit: a few things that I'm not sure about. When I view the properties of my internet connection i see
"Authenticate as computer when computer information is available" checked and
"Authenticate as guest when computer information or user is unavailable" unchekced.
I have a local area connection and a 1394 connection.