You can't get compromised through a port that isn't open. Use ps and netstat to see what services are running. If not sure, then they should not be running. Then take whatever steps necessary to make sure they don't start again on the next boot. See your distribution's documentation on this.
Many distributions start some well known services by default.
You may not have done anything yourself explicitly to start these. And may not even realize these are indeed running. But it is up to you to know what is running, and how safe it is. Chances are it isn't. If you decide some services are essential, make sure you are running the most current version.