Looks like your old system is looking for that system as part of it's startup. If I had to guess, you off-loaded some of your information from your work computer, and inadvertently included some of the system settings as well. Most likely, it's just annoying, not something that will affect your using it. A wild guess is that the other system is set up to connect to a main server, and obviously your new system isn't using the same network, so when it tries to connect (to reach databases, system-wide updates, etc.) it's lost. You should be able to fix this easily enough, simply by browsing through the various network settings available to Gnome. (Which one is affecting it is a little hard to guess, as it could be MS-Windows/Samba related, Netware, or another of the dozens of network OS's out there.)
While you could edit your /etc/hosts file (and put in a "dummy" computer, looping back to your own system) to "pretend" to connect to the desired system, it will most likely result in other errors, because even when it "thinks" it's connecting, it won't receive the correct responses to it's requests.
On the upside, once you figure out where/what the problem is, not only will you understand Linux/Gnome's networking process better, but you'll even have a bit of insight into the network used at the location where your other computer is located.
