Sometimes users might have issues with connecting to TFS, either the web interface or through Visual Studio. Below are some of the commonly errors I see.
First step to troubleshoot is to see if other users has the same problems, then verify that the use has access to other resources in the network, like fileshares and internet access.
Common errors and reasons:
-The user password has expired in the domain.
-The user connects from another domain and has wrong credentials stored in Windows credential manager.
Unable to connect to the remote server
-DNS issues. Verify that DNS resolves to correct IP of server. Some people tend to add entries to the hosts file, so be aware of that.
-Proxy settings. 3.part debuggers like Fiddler modifies the proxysettings and can cause network issues if not closed correctly. Start/stop Fiddler to solve it.