It depends.  How were you preparing your return, and do you have any backup?

  Do you have the desktop software (CD/download) and were preparing the return on your computer as opposed to using Online TurboTax?   If so, all return files are stored on your computer and possibly a backup device (if any.)  Was all your data destroyed with no backup?

If you were using Online TurboTax, however, then it won't make any difference.  You can still access your Online return through your new computer since that's done through a browser.

When I use the desktop version, I make a backup copy of my return's data file to a thumb drive at the end of each session--just in case.  Then I also make periodic backups of my hard drive as well.