Any chance over the last two years you chose to create a Microsoft Office Account for storing backups etc?!
When Office 2013 came out Microsoft had begun storing Product Keys is a new way to reduce piracy and in one foul swoop make the thousands of websites boasting to have 'free' product keys useless.
The actual product key if found via any tool will only display the last 5 alpha numeric characters accurately.
The full product key can be found inside your Microsoft Account on Microsoft's servers.
The only reason you can access those last characters is to help you select the correct product key in the event you are the legal owner of multiple Microsoft products, and therefore have more than one product key listed in your Microsoft Account.
The Dell website article I pointed you to suggested calling Microsoft to activate your Office installation.
There is a reason for that suggestion:
- If you have the Product key of a Microsoft certificate or sticker stuck on, or inside the computer case, then simply citing this allows Microsoft to verify you are the legal owner of said product.
- Secondly, in the event you lost that certificate, or are unable to read it [ e.g. you are legally blind ], then they can give you a brand you product key [ at no additional cost ] after you provide proof of purchase [ which they can tell you what they need as proof ].
My gut feeling is that if someone was selling Computers in 2018 with a 2013 product installed that now is not supported by Microsoft, then that someone was probably a fraud. Unfortunately, you may in fact need to buy a new license, if you wish to continue using Office 2013. If that is the case, it'd be a better investment to purchase a license for a more recent Office product that still is eligible for security updates and any 'fixes' that may be created to resolve issues created by the ever developing status of Windows 10.