After poking around for a few minutes several facts became clear:
1) At least one GPIB interface has a hard ethernet connection (and does not currently go through the wireless).
2) The wireless on the laptop works fine, since it can connect to the router.
3) The rest of the martian network cannot talk to the router.
This led to me replugging the ethernet cord back into the wireless router, which at some point in the past had been unplugged. The computers now seem to be happy and can talk to each other.