You should have posted this in the P2P section, but hey what the hell.
Often it's a case of using the default port that is the problem. ISPs are known to strangle these so the advice is always to use a non-standard port above 49000. In Azureus this is Options & Connection. Set the incoming TCP listen port to a number above 49000 (& below 65000). Then if you've a firewall you may have to open the port in that also , likewise in a router/adsl modem if you have one.