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

Have you done the port test (it's in the sticky)... what's the result?
http://www3.limewire.com:6346

Do you see the firewall icon (brick wall in front of the blue earth)?
Within LW, go tools > options > bug reports > view example. Scroll down to 'recieved incoming this session'. Is it true or false?

Exactly what fixes have you tried from the connections sticky?