Incorrectly Sees "Multiple Networks" Can't Connected

I have a wired router connected to a combination wired/wireless switch (both are LinkSys and pretty old). The PC in question has a wired connection to the switch. In the Network and Sharing Center, Vista sees two Networks: Network (private) and Unidentified Network (public), but both have the same IP information. Both also say local and internet access, but I cannot connect to the Internet. Disabling one of the active connections (one of the fixes suggested by Windows) causes all network connections to be disabled. I have tried resetting the router and switch, renewing the DHCP lease and resetting the network adapter to no avail. The most frustrating aspect of this problem is that it is intermittent. Sometimes, without apparent reason, the computer will "just work." There is another Vista PC also with a wired connection to the switch that has no trouble connecting to the internet and correctly sees only one network.