You don't need to do a backup and restore. You can just directly import the old .ftw format, as shown here:
http://ancestry.custhelp.com/app/answers/detail/a_id/3673/kw...
After you get your new datafile into your new computer, buy FTM2012 and open it with that.
http://ancestry.custhelp.com/app/answers/detail/a_id/3673/kw...
After you get your new datafile into your new computer, buy FTM2012 and open it with that.