I don't use windows or cygwin, so I'm making assumptions about how unixy a setup it provides you with. In a real *nix machine the following should work.
First open a tunnel from port 6666 on your own machine, pointing to port 6666 on the gateway machine. This will also give you a shell on the gateway machine. Then using this shell forward port 6666 on the gateway machine to port 22 (ssh) on "computer1" (where the files are).
windoze% ssh -L6666:localhost:6666 firstname.lastname@example.org
gw.dest% ssh -L 6666:localhost:22 email@example.com
Now in a 2nd terminal on your own machine you can get directly to "computer1" (machine behind gateway) by sshing to port 6666 on the localhost (your ownmachine). In this context "localhost:6666" can be thought of as the ssh server on the machine behind the gateway.
windoze% scp -r localhost:6666/path/to/directory/on/computer1 .