Xcuse some of the repeat questions but this is a standard list:
Can you give us a total desciption of your set up:
1. OS version? (eg: Windows 98)
2. What firewalls you have?
3. How much 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.

Use only one firewall! 2 can interfere with each other! To configure for LW see: http://www.limewire.com/english/content/firewalls.shtml

Try this test & try other port no.'s, what you do is type the port no. in & press the jump button & then press the Probe this port no.: https://www.grc.com/x/portprobe=6346

Wireless sounds it might be an issue. Please specify the brands & models of each specific device. And are you connected on a network?