Aha! That is the classic symptom of logging in as a user that does not have ssh privileges enabled in the Control Panel.
By default, DreamHost does not enable ssh for users, only ftp. You can correct this by logging into the control panel and navigating to the Users -> Manage users screen, selecting the "Edit" link under the "Actions" heading on the right side of the screen adjacent to the user you are logging in as, and selecting the "radio button" for "Shell account - allows FTP plus ssh/telnet access."
Submit the changes, wait a bit for it to "take", and try logging in with putty again - it should work now. There is information on this in the DH Wiki article on Enabling Shell Access (which is linked on the DH wiki article on SSH - second paragraph).
I suggest trying to troubleshoot your shell access; so many things are so much easier when you have that working, so it is worth the time to get that straightened out IMHO. Once that is done, the shell command "cp" has you covered.