I can tell you your Thompson modem uses a NAT firewall & will need to have a port forwarded for LW. Can you tell us the model number?
I have multiple versions of LW on my mac. Though I don't recommend going backwards in versions b/c it can stuff up your dwnld prefs.
Try this beta version:
http://www.mager.org/LimeWire/ (choose the http link & don't use Explorer to dwnld it!) It is a beta version & although it has a couple of xtras, the media player is disabled (but with iTunes you shouldn't be too worried.) This version may well sort things out!
If so, can we get your modem port forwarded to allow 100% access thru the port 6346? Give us the model no. & I'll give you the instructions.