I can't imagine anyone even trying to  use an HP disk on a Dell. I
suspect you'd get nowhere at all.
When I get stuck, I use my OEM disk and the Windows license key on the
computer in question.
This seems to be controversial, and windows licensing seems to be quite
arcane.

I also service Dells (and others) for a living. The Company specific 
installs of Windows usually contain chipset and other drivers that are 
specific to that brand of computer. If you install say an HP branded 
windows on a Dell, you'd have some drivers to fix before it would work.

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