rp88, please allow me to spare you the troubles, the key that Belarc displays is not the Windows 8 OEM key that shipped with your computer. Some of the other keys on there where you installed the software, such as Microsoft Office, will be the correct one that you keyed in by hand & just this weekend, I reinstalled both Windows 7 & Dell OEM Windows 8. My Windows 7 & Office 2010 COA's (keys) were correct & all worked fine. I used my Dell Windows 8 Recovery DVD to install that OS, no key was needed, it's in the UEFI. Trust me on this one & don't bother. If you have the right media, no key will be needed.
Neither is the one that Speccy reports correct. If your computer shipped with Windows 8, it has a UEFI motherboard, which is the replacement for the older BIOS type ones. While many still prefers BIOS, those days are officially gone on computers that shipped with Windows 8 & many that shipped with Windows 7 has been shipped with these for a year or so before Windows 8 was released. The main difference here is that Windows 7 is incapable of Secure Boot (the last time I checked), some LInux OS's has the key (that $99 key that many interpreted as a joke, with the rest of the article), in the Privacy and Security Topic in the Speak Easy section.
Back to the UEFI. That's where your "real" key is. You should create a Topic in the Windows 8 section for assistance on this, as you'll get more accurate responses from those who has used the legitimate tools (as Animal described above) to locate your key. Plus we don't want to turn this Topic into another one altogether.
In another Topic recently, I advised you on how to create a recovery disc set, all that was needed were 3 to 5 blank DVD's, the -R type is what most burners of today are compatible with. You can also use a 16GB Flash drive on many computers to do this same thing, and unless corrupted, there's a keyboard shortcut at Startup to load the Recovery process. On some computers, this may be s shortcut in the Start Menu, System Recovery (or similar wording). The system will reboot & begin the process.
No key will be needed if you have any of these options. If this isn't an option to you, you'll have to create a new Topic on the issue in the Windows 8 section of the forum.
Thank you for your understanding in this matter and for being a valued member of BC Forums.