copy your steam/steamapps/common folder over. Click install and it will rebuild the files, but wont need to download again.
Google will tell you where saved game files are stores though.
Wyvern and I tried all sorts of ways to get her steam working after removing a drive. Eventually we had to plug it back in to get it to work. We did not try that method though.
Simply delete the steam install folder, run a registry cleaner and re-install, then take the backup and install it again.