Unfortunately, I had done this and still cannot get a working installation of the Defender engine or updates. Repeating your procedure shows:

“No engine/signature is currently loaded.”

Then, Windows update result:

“Security Intelligence Update for Microsoft Defender Antivirus – KB2267602 (Version 1.363.1354.0) Status Installing – 100%”
THEN:
“There were some problems installing updates, but we’ll try again later. If you keep seeing this and want to search the web or contact support for information, this may help: (0x80070643)”

This happens repeatedly. I have done a Windows 10 Repair-Install / Reset, without success. I’ve cleared numerous installation files as recommended by numerous sites that profess an answer.

SFC /scannow and DISM /Online /Cleanup-Image /ScanHealth both come back clean.
I’ve even run McAfee’s MCPR.exe just in case there was some hidden virus protection installation (I never have used an alternate to Microsoft’s anti-virus).

I have run out of options. Adding another company’s anti-virus has always been suggested — I don’t see why this should be necessary. No Microsoft solution has fixed my problem — clearly a BIG BUG. Other people with HP laptops seem to have had this issue with no solution.