NT Service\MSSQLSERVER is the default account when installing SQL Server. It's a managed service account (MSA), and should be fine. I should also have the necessary permissions.
It seems to be configured to start automatically, so it should be running, but you cannot start and stop it yourself.
Anyway, you need to talk with your IT folks, since you don't even have access to the locks. Maybe they did something wrong.. They could post to this thread, if they need assistance.