I just ran auto-update, without an effect on the chat applet.
I am behind a linksys router. While it does have a built in firewall, I have enabled the 'DMZ' option, which forwards anything sent to my real IP straight to my PC. With this I am able to run an FTP server, use file sharing (eMule), and connect to my pc via Remote Desktop, without forwarding any specific ports. I have had no network issues since I enabled it (although I have thought of turning it off and using old fasioned forwarding for better security). I suppose theoretically there still is a firewall. I have no idea how Java communicates, so perhaps it is still encountering firewall functions, but everything on the router besides DMZ is set to default.