Hello Mark,
Thanks for visiting us on the Forums with your question. I researched the .PQI file extension and discovered these were most likely created by a program called Power Quest Drive Image 5.0 or possibly an earlier version.
Related article on software.
Related article on downloading software.
You may need to use an older computer running Windows XP, worth a shot on Windows 10.
Once you have the program installed you can then interpret or uncompress the files you have backed up.
Lastly, on Archive.org I found a copy of the bootable media that would allow you to browse the data files you backed up.