Do you see the firewall icon (brick wall)?

You've tried 5 p2p apps & none of them are working well... doesn't sound good. I can't find any evidence that your ISP's currently anti p2p, if that was the case then your download speeds would probably be woeful. One thing you could try is deleting the LW preferences folder (when LW is properly closed). I'm not sure that it's gonna help, given that you're having the same probs with other apps but... give it a go. See points 2 & 3 below for instructions
Fixes for LimeWire

What are your details (excuse the repeat questions!)

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