To some extent it depends on how your buildings are linked.
If the phone company is doing it for you, check their equipment for power and connect lights. If you don't have the light pattern you have come to expect, call for service.
If you link your buildings with FDDI or CAT-5, check the hubs at each end of each connection. Are the hubs powered up, and do you have a green light at each end for the connection of the inter-building link?
For each inter-building link that seems to not work, if you are getting lights on the hub, find a station plugged into that hub at each end, and see if those two stations can ping each other. If so, the link is up, and the problem is elsewhere. If not, your problem is the cable or one of the two hubs.
For FDDI, you should have monitor lights on the fiddi connections at each end.
Moving along your network, for each hub, pick a station and make sure you can ping and connect to the server. When you move out by one connection and can no longer connect, carefully examine EVERYTHING between the station that worked and the one which did not. That connection has a problem.
Good luck.