I've tried reinstalling Limewire four or five times. Still nothing changes. I'll double click the icon, and the hourglass appears, then disappears. The program doesn't start. I've tried installing the latest java, but that doesn't help me any.

Try deleting your LW Preferences folder whilst LW is closed; instructions here: Fixes for Limewire

If you still have problems then there is an alternative installer I think. You just unzip it & use it. See Here about other version.

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.