Apologies for taking so long to respond. The email filter gremlins have attacked again.
The ‘Select VCS project’ button is used by legacy File based source control. This is usually enabled if the ‘Default VCS Provider’ is selected in ‘Options - Source Control - Default VCS’.
It is possible to have Team Coding enabled without having this option set, as it is a separate module.
This is the first thing I would check.
This button may also be disabled if you are connected to a Team Coding enabled database and one or more of the Code Collections for Team Coding is a ‘Files’ type (i.e controls scripts instead of databases). In this case toolbar actions are handled by Team Coding and not the desktop source control settings.
If neither of these answers your question, please send a little more information about the users configuration.
I hope this helps