Windows Activation fail, now what?

I have a Precision 5530 and a few days ago it failed to boot. The message was something about no hard drive found. Tried again, same message. I shut it down, unplugged all USB drives, and started it again; this time it booted normally, but I got a warning that the hard drive was going to fail. Support Assist said that S.M.A.R.T. reported a hard drive failure and I needed to replace it ASAP. I did some online research and indeed that particular S.M.A.R.T. error means the drive hasn't long to live. So I bought a replacement, followed Dell's instructions for re-installing Windows, and now Windows Settings is telling me it can't activate Windows because "Windows reported that the hardware of your device has changed. Error code: 0xC004F211"  Well, of course the hardware changed, the hard drive failed and was replaced. So how do I get an activation code? I certainly shouldn't need to buy a copy of Windows, but that seems to be my only option.