Membership of the sysadmin server role gives you system administrator privileges within the SQL Server instance.

It does not give you any permission at all on the server. If you are currently able to log into the server, you are lucky - a Windows admin has granted you the rights to log in.

If you want to be able to start and stop services through Configuration Manager, you need to be a member of the Administrators group on the server.

Actually that last statement is not 100% true - there are ways of giving your Windows account more granular permissions - but my point stands. Server permissions and SQL Server permissions are unrelated.

Hope this helps.