Can you give us a total desciption of your set up:
1. OS version? (eg: Windows 98)
2. What firewalls you have?
3. ram?
4. Hard Disk space available?
5. Connection type? (eg: dialup, broadband, cable, etc.)
6. Modem & router brand name & model numbers?
7. Where are you trying to connect from (home, school, work, etc.)?
8. What version of Limewire (LW) & Java do you have? (Go to LW's menu Help>About LW...) Will show both LW & Java version.
9. Who is your isp provider?
10. Is this a your 1st try at LW or is this a new problem with an experienced user.
11. Approx. how many incomplete files do you have?
12. Approx. how many shared files do you have?

Describe in detail what you do after you open LW. Do you use the Resume/Find sources function on all your files ... this can cause side-fx.
Also, after opening LW it should be left to settle for some time before using. Depending on no. of incomplete & shared files this should be 10, 20 or 30 mins.