I also have the same exact problem!

internet connection? T1
router? yes
firewall? yes
OS version? 10.2.6
limewire version? PRO

Although I am behind a firewall (at work), this problem started suddenly and without change at all on my end. I have the same problem at home with my 56K dial-up connection where there is NO firewall. I'm using Explorer for a browser in both places.
I also had no problems installing, but the light goes green for a second then goes back to red when I press connect. Please help, I'm so frustrated!

What's more, is that when I finally DO connect, I am rarely successful in downloading anything. Many times, things will start downloading, and then say "Could not download; awaiting more sources".