I really don't want this thread sink in vain like all others that I can find from Google.
I used the 'sa' account and SQL Server authentication to connection from my workstation to the server and I believe 'sa' has sufficient privilege to start, stop or restart the SQL Server service.
I also tried remote desktop the server directly, log on to SSMS by 'sa' again and the green arrow appears fine.
Its got nothing to do with being able to start/stop the services, its all to do with if your windows account has access to see the services state. go to start, run and type services.msc, change the machine name to the server your connecting to in ssms and see if you can see the sql services, i bet you wont be able too.