Are you saying you can't login (shell) to your old host?
There should be a bunch of ways you can do this but without shell access to your old host your options are somewhat limited.
You might be able to (logged in to DreamHost shell) ftp to your old host, turn off interactive prompts (prompt) and mget *.
I'm not sure if that will properly handle ascii/binary or recurse subdirs though.
You can tar/gzip your root directory on your old host (assume *nix) then FTP out and untar/gunzip.
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