Why don't you network the computers via an ethernet card. Else move them via burning to a cd/dvd-rw.

Direct Connect search type via LW won't work if one of the computers has a firewall that isn't configured properly to allow LW full access. You should be able to see the ip of the computer at the top of the Direct connect search box. If it's missing on either computer then you have a firewall issue. I wonder also if both are using the same ip.