What happened when you left LW on for some time? Did it show any signs at all of going past one green quality connection bar?

You can try these things: Within LW's prefs:
1. Prefs>Speed & disable Ultrapeer abilities by ticking the option box. You may want to at least temporarily change the connection type back to say cable or something.
2. Prefs>Connections & untick the Connect on startup option box.
3. Prefs>Advanced>System Startup & untick Start on system startup.
Don't forget to press the Apply button after all of these changes.

Quit LW. Then open again. Now go to the LW File menu & select Connect. Leave LW running for some time. If it doesn't work select connect again.

Failing this, install the Standalone Java version For some reason this can sometimes make a difference. After installing do a SAFE start & Repair permissions (which is what you should do both before & after installing any softw.!!

Try again with LW & allow it some time to get it's connection.

If that fails again after several attempts, try deleting LW's preferences called .limewire & found here: /Users/your_username/Library/Preferences/LimeWire (Note that all your settings will be lost so you should make a note of them beforehand.) And try connecting again.
If still not successful, get back to us.