I do not think that Compass is meant to be run as a service. It is a client application. Perhaps you are confused between Compass, then client, and mongod, the server. The latter can be run as a service. But it is not the same download.
It fails to connect because mongod, the server, is not running.
To install and run mongod, see
If you still fail to connect, then perhaps, you will be better served with Atlas: