Can you give us a total description of your set up:

1. What firewalls you have?
2. Connection type? (eg: dialup, broadband, cable, etc.)
3. Modem & router brand name & model numbers?
4. Where are you trying to connect from (home, school, work, etc.)?
5. What version of Limewire (LW) & Java do you have? (Go to LW's menu Help>About LW...) Will show both LW & Java version.
6. Who is your isp provider (Internet Service Provider)?
7. Are you sharing the connection with other computers or p2p sharing programs? If yes, please give details of set up.
8. Do you have a lot of incomplete files? Go to your incomplete folder on your hard disk drive & tell us whether the no. of incomplete files in that folder are (a) less than 500 (b) up to 1,000 (c) between 1,000 to 2,000 or (d) over 2,000 ?
9. After opening LW, do you use the resume/find resources function on all your files?
10. How much ram & Free HDD space do you have?

* You could try deleting your LW preferences folder whilst LW is closed found here /Users/your_username/Library/Preferences/LimeWire
Make a note of important settings as after you do this process, you'll need to reset option settings after re-opening LW.