It sounds like you're trying to connect to fake files, they're pretty common if you're searching for new releases & really popular files. Do the files you're trying to download have heaps of sources (up to 100)?? Stay right away from these, go for a file with 10 sources or less. Vary your search terms, try the All Types search & search at different times of day, when hosts in other time zones are online.

For your firewall, read through this
Connection problems? Check here first!
Don't turn your software firewall off, just configure it to allow LW access. If you have a high speed modem/router, it probably has it's own internal firewall. You'll find heaps of info about using UPnP & port forwarding to overcome firewall problems in the thread above If you're stuck, post 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