Check to see if your new ISP has any type of blocking system and check to see if your router has an inbuilt firewall, ask them also if there is a recommended method to setup your new router so that peer to peer traffic will work. After you've checked those things and if the problem still persists try the regular problem that a lot of people seem to have and renew your gnutella.net file. If you have a firewall sometimes you will find that your router and the AV application both have firewalls which can be a problem. Only one firewall at a time should be active. To check the gnutella.net possibility look under any of the "stickies" that go with that section of the forums. But if you were having problems before you eve installed Limewire I'd suggest it's got something to do with your new router and it's setup and may be worth investigating the various options it has for allowing internet traffic and see if you can come up with an answer in that direction. I've just found out that apparently ARES is connected in some way to the gnutella network and this common feature with Limewire may be a good indication to try the gnutella.net route and see how you go.
If you're running Vista you will have to go into the App Data folder which is a hidden folder until you go through the control panel and folder options section then in the view sector reset the option to show all folders and files then go back through C\:User name\Roaming\Limewire and replace the gnutella.net file with one you have downloaded from a recommended site found by reading that section (Connection problems) in the sections of these Limewire forums.
Good Luck!