Just to check, you might try 
FrostWire or 
Phex to see if you have the same problems. Some people find that by installing FrostWire it connects, then LW will connect. The newer versions of LW have been a bit on the buggy side so FW or Phex are nice alternatives. 
 
Steps 1-6 here are worth trying 
Fixes for Limewire (click on blue link)