Any java applet in your brower is running on your PC so it has the same restrictions as any other application (ie the firewall).
To get through a firewall that only allows 80 (http) and ftp (21) you will need a server on the other side which can redirect ports. BTW you can proably also user port >1024 as that would be required by ftp
Example of port redirection
A---80-->F---80-->B----23->C
A is your machine, F is the firewall, B is the redirector and C is the target machine. basicaly machine B take data in at port 80 are sends it out via port 23 to machine C. The ports between A, F and B dosn't need to be 80, it should be possable to use any port above 1024. B would have to be a machine that you have access/control of.
A search in google for 'port redirector' will find you a selection of hits, or for windows users try
http://www.foundstone.com/knowledge/free_tools.html for a free port redirector and a heap of other tools.