As Birdy suggested, try a fresh connection file. This is a likely issue. I have not created connection installers for linux because I thought the concept was easy enough to manually replace the file and was not sure how much demand for a linux connection installer would be. ie: download a fresh gnutella.net file, go to your Home folder, either ~.limewire or ~.frostwire folder and replace the gnutella file inside.
Keep in mind if using LW 5 and the gnutella file's modification date is older than 28 days then LW will delete the file as it opens. But I produced a linux LimeStart for LW5 to solve this issue. I have Ubuntu 12.0.4 and LW 4 and LW 5 connect fine.

Also keep in mind that for LW at least, you may see a no connection message on the main window. This is because the main window connected to the original LW site which no longer exists. All that matters are the connection bars bottom-left-corner of the LW screen. sample image.

One of the tricks I used to use for LW4 was to disable one of the advanced settings such as either DHT and TLS, I can't remember which one seemed to work for me. Otherwise it seemed to have connection/firewall warning issues.

If still no connection you could try installing Phex to see if it connects. There is a Phex connection installer for Linux. (I created a connection installer for Phex because it does multiple things.)

Edit: Fixed the Filecloud, MediaFire and Rapidshare broken links.