Welcome to the Community, KlKlKl! Let me help you download QuickBooks so you can get on top of your tasks.
As long as you still have your license and product key information, you can download QuickBooks Desktop Premier 2013 here. Just take note of these system requirements to ensure the software runs on your new computer. First, the operating system must be Windows XP or a later one. Also, the computer must be 64-bit with at least 2.5 GB hard disk space for the setup and an additional 250 MB during runtime. You'll also need 2 GB of RAM, a screen of at least 1024x768, and a processor of at least 2 Hz.
Furthermore, I'd like to inform you that access to QuickBooks Desktop Payroll, Desktop Payments, live technical support, Online Backup, Online Banking, and other services have been discontinued in the product you're looking to download. This also means you'll no longer receive critical security updates. For more info about this, refer to this article: QuickBooks Desktop service discontinuation policy.
You might want to upgrade to a newer version of QuickBooks Desktop. Here's an article to guide you on how to do it: Upgrade QuickBooks Desktop Pro Plus, Premier Plus, or Enterprise.
Let me know if you have any other installation concerns in QuickBooks. The Community is always available for you, KlKlKl.