Open a Command Prompt as Administrator and run the following command:
netstat -abno
This shows the bound port numbers as well as established connections. In addition, this identifies the process id associated with each row. If the list is long, sometimes I direct the output to a file so I can search for the port or process ID I'm interested in:
netstat -abno > c:\netstat.txt
To use the -o option, it must be run as Administrator.
I then like to use the Resource Monitor to identify which process ID. (Within Resource Monitor I can look at the file handles for the process which give a pretty good clue of the application.)