This sounds a lot like a problem with your DNS lookups. It's possible they are not configured correctly (via DHCP, or static IP, possibly), but I'm not an expert on resolving DNS lookup issues.
Your first movement on this should probably be to call your provider (your ISP if you're using cable/dsl/dialup, or your network admin if you're going through a business connection) and see if you can get some help on this. It may be that the DNS server that you're getting (through DHCP or manual configuration) isn't valid any more, there may be a failure on that server, or some local configuration problem. The support center for your provider will hopefully have some troubleshooting information and can help with this problem.
