AFAIK, Firefox uses the underlying OS resolver, so it should work if nslookup works. Chrome has a built-in resolver, so all bets are off there.
Start a clean Firefox profile and see if you can get anywhere with it. (Run firefox.exe -p to bring up the profile manager.)
Unless you have file sharing totally disabled, see what happens when you run "net show \\other_computername" from each PC. (Substitute the name of the target PC for other_computername.) I'd expect to see at least an empty list, or an $IPC share, not an error.
Start a clean Firefox profile and see if you can get anywhere with it. (Run firefox.exe -p to bring up the profile manager.)
Unless you have file sharing totally disabled, see what happens when you run "net show \\other_computername" from each PC. (Substitute the name of the target PC for other_computername.) I'd expect to see at least an empty list, or an $IPC share, not an error.