How do I obtain my Window 7 product key from Dell? Reverting back from Windows 10

I have the same problem with an Inspiron 11Z 1121.  It's a great little laptop, but I'd like to reset it back to new setup and sell it.  Can't do that without the OS?

You need to use a Dell Windows 7 Reinstallation DVD or media made (in advance) with Dell Backup and Recovery which will use Dell OEM System Locked Activation. i.e. activates automatically when installed via a Dell BIOS.

well, I have neither. I can download Windows 7 on another machine, but without the product key it's useless. I can not get the laptop to boot, so I can't get to the dell recovery screen. I tried pushing f8, nothing happens.  I also tried the Windows 10 recovery disc, but it tells me the drive is locked.  I'm starting to believe this windows 10 was a big scam.  All I want is the product key I purchased with the laptop so I can reinstall 7.  I have tried to fix 10 for 2 weeks and I have given up.

You cannot download Windows 7 because Microsoft removed the Digital River .isos and made a Microsoft Software Recovery Tool which blocks Dell OEM keys. i.e. even if you had the key you would be unable to download Windows 7.

You should have followed the Dell Backup and Recovery Prompts to make Recovery Media when you got your machine or at the very least made Recovery Media before the Windows 10 Upgrade.

The Dell OEM license as mentions uses Dell OEM SLP activation. This can be applied using Retail Media if you have a Windows 7 Retail .iso however the problem as mentioned is in obtaining the .iso. See Part 6 Variant D OEM with Retail Full Media (Unofficial):

http://dellwindowsreinstallationguide.com/a-clean-install-of-windows-7/windows-7-installation/

If you are out of warranty it may be difficult to procure installation media from Dell.