A family of Microsoft spreadsheet software with tools for analyzing, charting, and communicating data.
Hi Luna, unless your Office 2013 came on CD you cannot use the Product Key to reinstall your Office on your new PC. Rather you sign into Services & Subscriptions of your Microsoft Account. Here is a direct link>https://account.microsoft.com/services You need to sign in with the same Microsoft Account that you used with the Product Key to setup Office for the first time. Please note that Microsoft no longer supports Office 2013, so you need o be very careful as you will have no security updates.
You can access Services & Subscriptions from this website> Go to the top right hand side of this page>Click on your name/avatar>My Microsoft Account (you may need to sign in again)
PS: I suggest that when you have both computers turned and online when you transfer your Office to the new computer, so that Microsoft can see you have uninstalled Office from your old computer. This may mean that you will not have activation problems, hopefully.