‘The Site Server cannot be contacted or trying to connect to an incompatible Site Server version. Please enter a new Site Server Name’ error when trying to connect to a different ConfigMgr / SCCM 2007 Site Server

When I try to connect to a different Site Server from within the Administrator Console I get a “Database Connection Wizard” error dialog box which states:

“The Site Server cannot be contacted or trying to connect to an incompatible Site Server version. Please enter a new Site Server Name.”

If I click the “Details >>” button the dialog states:
“The RPC server is unavailable. (Exception from HRESULT: 0x800706BA)”