Hi Jane, Have you installed your Premier 2013 on to the new computer as yet?
If not, here's what I'd recommend to install your software on a new PC.. firstly before making the move, firstly rebuild & verify your file to ensure there are no errors in the file. Follow up on any if there are after this process is completed.
Create a few backups and transfer one to a removable disk eg USB stick, external hard drive.
Uninstall Reckon Accounts from the old PC then install on the new. If you need to access your software download, you can do so from the Members Area which is here - http://members.reckon.com/Login.aspx and go through the prompts to install and register.
Let us know how you get on or if you have any questions.