If the other computer is different like Mac or Windows you have to ask for the other download. Or what happens when you try to download it again? I downloaded it to my Desktop and Laptop. Do you see the download in your account? Or did you already first install it from the CD? You can't do both CD and Download.
Access your downloads here
https://shop.turbotax.intuit.com/commerce/account/secure/login.jsp?pagecontext=download
If you can't find your download, use this TurboTax account recovery website to get a list of user ID's for an email address. Run the tool against any email addresses you may have used
https://myturbotax.intuit.com/account-recovery
