What if you connect another computer to the switch where you are having the issue? What if you connect one of the computers that have the problem elsewhere in the building? What if you bypass the switch in the room and connect a computer directly to the incoming cable? On the machines that aren't working, is the gateway address set correctly (should be your router's IP) and can you ping this IP from the faulty machines?
It would also help if you described how the rest of the network is configured including what hardware (in particular models of switches, routers.etc) is being used.