The service 'mssql$act7' isn't the service that you need to have started, the desired service is 'SQL Server (ACT7)'. If you do not have this listed in Services, it did not install correctly and back to the SQL Server install failing.
Is 'SQL Server (ACT7)' present in Services? If yes, will it start? If it will not start, are there errors for it in the Event Viewer?