The other day I came across an interesting research project that claimed to identify individual computers without cookies just by analyzing O/S, browser, screen sizes, fonts, and some more data that is sent by the browser as part of the page request.
I tried it myself, and yes, IIRC my computer setting was unique in a database of 600,000+ computers. Scary. (Unfortunately, I did not bookmark the site, so I can not reproduce a link.)
So actually, you should not even use the same computer to sign up for a new account.