If it's a sudden problem, it might be related to your LW preferences. Try deleting your LW Preferences folder whilst LW is closed; instructions here: Point #2 & 3 in Fixes for Limewire (sample image included at bottom of page.)

If you are having problems because you just updated your LW, then chances are it's due to LW's firewall detection technology. This is good for the network as a whole ridding of the problem of users with unconfigured firewalls which is not good for other users trying to connect to them. So if you did just update, check the link Birdy suggested; Connection problems? Check here first! (click on link)

The problem might be your software firewall or else, it might be your modem/router. Most high speed modems have internal NAT firewalls. To configure them you have the option of UPnP or manually port forwarding depending on your brand & model.