Are you certain the optane module is what failed -- and not the hard drive?

@ejn63, Yes. The NVMe error at the system startup stopped showing up once the failed Optane memory was removed. The System Diagnostics does not detect any hardware problems. I am also able to view the content of the HDD when I connect it to another laptop. Based on these, I believe the HDD is fine. It appears that the system was originally configured to boot with Optane and HDD paired together, and that the new Optane memory is not configured to work with the existing HDD.

I read this post about a similar issue that you participated in: https://www.dell.com/community/Inspiron/Dell-Inspiron-15-5000-5570-HDD-failure-and-poor-customer-support/m-p/7541106. It seems that changing SATA settings in BIOS from RAID to AHCI helps with recognizing the HDD but I would like to know if there is a way to pair the Optane memory with the existing HDD without formating it and having to install a new Windows. I have an image backup of my system with all the partitions.

You need to get the system booted before you can disable the Optane cache.  

https://www.intel.com/content/www/us/en/support/articles/000024626/memory-and-storage.html

My recommendation is that if you have a full backup, ditch the Optane module and hard drive and replace them with a native SSD - restore the image to that, and see if it'll boot.  If it won't do a Windows 10 repair install.

https://answers.microsoft.com/en-us/windows/forum/windows_10-windows_install/how-to-perform-a-repair-upgrade-using-the-windows/35160fbe-9352-4e70-9887-f40096ec3085