You can use a generic key to install but not to activate.
Unless the key is in bios you don't have a windows 8 key.
Windows 8 keys are encrypted stored in the Bios installed at the factory. There are no more COA Stickers due to piracy. (OEM System Builder Versions Do Still have COA Stickers)

Windows 8 now comes with a Genuine Microsoft Label there are NO MORE Certificate of Authenticity (COA) Labels.See the following examples of labels to look for.Color-Shifting Ink The color shift on the label is designed to change from one color to another when viewed from different angles,making it easy to determine if it is genuine.Windows 8: magenta to greenWindows 8 Pro: blue to purpleWindows RT: turquoise to purple
Genuine Microsoft Labels
You could try Belarc Advisor.
I don't know if this shows the key or not. (Versions Higher than 8.3c do Show the Key)Version 8.4 supports Windows 8.1
- Operating Systems: Runs on Windows 8.1, 2012 R2, 8, 2012, 7, 2008 R2, Vista, 2008, 2003, XP, 2000, NT 4, Me, 98, and 95. Both 32-bit and 64-bit Windows are supported.
- Browsers: Runs on Internet Explorer, Firefox, Safari, Opera, and many others.
However as you change versions by adding softpacks you should save the previous keys as they are removed and replaced with the PRO and MCE packs. But windows will not clean install with an update pack so you need the original key in order to Install clean then do windows anytime upgrades back to PRO or MCE editions.www.belarc.com/free_download.html
Download a windows 8 ISO and Burn to Disc.
Use the Generic Key to install and then Activate after Getting back online.
While you still can I would download a recovery ISO directly from Microsoft. Windows 8 Certified UEFI machines REQUIRE 64 BIT media for booting 7 or 8.
http://windows.microsoft.com/en-us/windows-8/create-reset-refresh-media
"Error 0x4001100200001005 if problem persists contact Dell support".
The reason you get Error 0x4001100200001005 is because the OEM hard drive was replaced with a retail hard drive. OEM drives are "tattooed" or branded and the DELL recovery media will search for it before installing. This is also why you cannot clone Dell Drives to new blank hard drives.
Generic Keys can be used to install but not activate.
XKY4K-2NRWR-8F6P2-448RF-CRYQH (Windows 8 Professional)
RR3BN-3YY9P-9D7FC-7J4YF-QGJXW (Windows 8 Professional with Media Center)
FB4WR-32NVD-4RW79-XQFWH-CYQG3 (Windows 8 [Home])
XHQ8N-C3MCJ-RQXB6-WCHYG-C9WKB (Windows 8.1 Professional)
GBFNG-2X3TC-8R27F-RMKYB-JK7QT (Windows 8.1 Professional with Media Center)
334NH-RXG76-64THK-C7CKG-D3VPT (Windows 8.1 [Home])
Dell oem Drives do contain a Dell DPN and other information Identifying them as OEM vs Retail.
Seagate, Western Digital, Toshiba. IBM and Hitachi DeathSTAR drives went to WD.
Technically there are only 3 vendors left in the world or as Highlander said. " In the end there can be only 1." My name is Duncan Macleod!

The 3 vendors will not warranty an OEM Drive vs Retail Drive.
In the old days you could clone the drive and get the factory reinstall image as well.
