Hi Stephen
Can you give us a total desciption of your set up: 1. Operating System version (eg: Windows XP), 2. What firewalls you have, 3. ram, 4. HDD space available, 5. Modem & router brand name & model numbers, 6. Where are you trying to connect from (home, school, work, etc.)?
These details are vital if you want us to find out what your connection problem is.

You will probably have firewalls on your computer right? For XP & some other common types see here: http://www.limewire.com/english/content/firewalls.shtml

Make sure you have a reasonably update version of Java: Java 1.4.2 (click on link) The LW installer will only install the minimum version which is Java 1.3 so I generally recommend to install with a later version of Java before you install LW. Java is very important for LW.