This video KB demonstrates multiple ways to determine the ports on which PowerCenter application services, say Integration Service and Repository Service, open on the server machine.
How to unassign services from an expired key and assign them to a valid key in 9.1.0 and 9.5.1
How to automate the repository and domain back up process for disaster recovery in PowerCenter
How to find in which host the Repository Integration service is running in a multi node domain