My guess is you have got a "restore" partition on your hard disk that contains Windows 7 (some computers shipped with a Windows 7 "image" on a spare partition so you can reinstall it easily if you wanted to). My Dell PCs all have a "hidden" image of Windows 7 on the hard disk.
And even if you upgrade to Windows 10 that restore partition will still exist on your hard disk with the Windows 7 "image" on it.
My guess is you have reinstalled that Windows 7 code from the Windows 7 image in the restore partition and overwritten Windows 10.
However ignore the suggestion from CrapatCryptics about buying a new Windows 10 from ebay.
The thing about Windows 10 is that once you have installed it (or upgraded to it) then Microsoft keep details of your computer on their servers. They upload details of your PC to their servers during the install process.
So your PC will ALREADY be registered as a valid user of Windows 10, so no need to buy it again.
This means that if you reinstall Windows 10 you DONT need to enter a code of any sort as Microsoft already know you are entitled to use Windows 10.
For this reason they allow you to download the Windows 10 code FOR FREE and reinstall it, no need to purchase it. This is from an OFFICIAL Microsoft web site
You can download the code HERE
https://www.microsoft.com/en-gb/software-download/windows10
You could try the first option on that web page, to upgrade the PC to Windows 10 (as you have already done this it will not cost you anything). See if it works.
Or you could try the second option to create installation media. This can be a DVD or on a USB memory stick.
Note that I don't think the Windows 10 code will fit on a "normal" DVD (it is too big) I think you need a dual layer DVD.
Creating a bootable USB memory stick is quite easy so try that, as long as your PC can boot from a USB memory stick.
Once you have the installation media you can then do a straight install of Windows 10.