From your description it seems like there might be an issue with the installation if the connector is missing from the server.xml file.
Do you have any anti-virus installed on the machine? (McAfee, Symantec) A lot of times anti-virus causes problem with ArcGIS Server.
You can try replacing server.xml from a working ArcGIS Server 10.4.1 to this ArcGIS Server and restart the ArcGIS Server service to see if it will pick it up? (Make sure you stop the service before changing the server.xml file)
To re-install you can do is,
- Uninstall ArcGIS Server 10.4.1
- Remove/Rename the folder Program Files\ArcGIS\Server
- Re-install ArcGIS Server 10.4.1