If downloading the whole thing would take you too long or if you have many 3rd party addons another method might be more useful for you:
- backup your RW folder in (default path) c:\program files\steam\steamapps\common\ to an external harddrive
- install Steam client on your new pc but
do not start it- copy the backed up folder into the directory (you may have to create it)
- start Steam and login to your account and hopefully you can start RW right away, if not verify the files through Steam (right click on RW -> properties -> local files tab -> verify game cache button)
another useful advice: write down your Steam username and password
