What are your details
OS(Win XP etc)
LW & Java version (help > about LW & you'll see)
Firewall you're using
Modem/router brand & model
ISP
Connection type (DSL etc)
Where you connect from (home, school etc)
Are you sharing a connection with other computers
Is this your first try with LW

Do this port test & tell us the result
http://www3.limewire.com:6346

Within LW go tools > options > bug reports > view example. Scroll down to 'recieved incoming this session'... is it true or false?

Make sure you're not running 2 firewalls at once. Double check that your firewall's configured properly (better to have 1 running & configured that none running!)
http://www.limewire.com/english/content/firewalls.shtml