Where do I find my Windows product key for the Dell Inspiron I bought at Microcenter

To find the Windows product key for your Dell Inspiron purchased at Microcenter, you can look in several places. Firstly, check the packaging or documentation that came with your laptop. The product key may be printed on a sticker or card. If you cannot find it there, you can try looking in the BIOS or UEFI firmware settings. To access this, restart your computer and press the appropriate key (usually F2, F12, ESC, or DEL) to enter the BIOS/UEFI setup. Navigate through the settings to find the product key information. If you still can't locate it, consider contacting Microcenter or Dell support for assistance.

Dell started to inject OEM license on motherboard firmware starting back with Windows 8.  So, Windows 7 product key for your machine would be located on a sticker affixing somewhere on the chassis.  If it's no longer there, someone may have peeled it off.

As for the Windows version upgrade transition, there were different ways to upgrade but generally, all of them had been expired with deadline from Microsoft.  

Where is your Windows 7 product key.

@Chino de Oro​ , thank you for the link to Microcenter's page "Where is your Windows product key".  It has the following paragraph:

"Computers that were originally licensed for a higher version of Windows, such as Windows 8, but that have installed Windows 7 by exercising "downgrade rights" authorized in their software license will not necessarily have a product key / Certificate of Authenticity sticker affixed to the system for the downgraded version."

I know that my system had been designed for Windows 8.1 (have a CD with my materials) but that had just come out so the computer itself had Windows 7 on it.  I am pretty sure that is why there is no tag on the outside of the chassis.  I have owned other computers where the tag is on the outside so I am familiar with that.  The only thing on this chassis is sticker declaring this is a Windows 8 Pro system.  Thanks again.

A Win 8 embedded license with downgraded Win 7 being installed would be the case for a customized order, not a retail desktop (because it would required the customers to pay for the downgrade).  But, to be certain, you can always find out if a Windows license was embedded.  When the available license finder tools failed to yield any result, you can make a Windows 10 installation key using Windows Creation Tool, Go through the setup as if you would installing Windows.  If the process asking for the key, then there is no key being embedded on the board.  If the system proceed to the boot drive selection, it (the installation process) found an embedded license and will be using it for the version of installation.

Try Belarc Advisor (free).

It will give you the Windows product key, but it may be Dell's generic key, not the one unique to your specific PC. The update to Win 8.1 might not accept the Dell key....

After searching the Dell and Windows forums, I found some mention of an app called ShowKeyPlus.

It is also in the Windows app store.  It is a simple .exe file that will find the Windows keys and is supposed to also show any Microsoft Office product keys.  I could not get it to download from the Windows App store but I did get it to download at github.com.  The github website also allows access to the source code.

This app worked and gave me the Windows 7 Pro installed Key and the Windows 8.1 OEM key.  As I mentioned, the computer had Windows 7 Pro installed and a CD with the Windows 8.1 upgrade.  Since the program is an executable, you can put it on a flash drive and run it without loading it on the computer.  There are some YouTube videos of the program too.