Most ISPs block the default port that Azureus uses. So it is a good idea to change Azureus' port number to something other than the default port. Here's a brief walkthrough on how to do that.
In Azureus click Tools in the menu at the top of your screen. Then click the Options link in the menu that drops down.
In the menu tree on the left hand side of this window Connection should be selected. Pick a random port between 49152 and 65535. Then enter that port into the Incomming TCP/UDP Listen Port box. When you are done, be sure to click the Save button at the bottom of the configuation screen.
Please enter the port you chose for Azureus below.