It is possible you have a failing hard drive in the Mini. Some types of hard drive failures can sometimes even keep the computer from booting properly to other media such as Internet Recovery Mode. See if you can boot the Apple Diagnostics.
If you cannot boot the Apple Diagnostics, then using another computer create a bootable Knoppix Linux USB drive using Etcher (Mac/Windows/Linux). Option Boot the Knoppix USB drive and select the orange icon labeled "EFI". While Knoppix is booting the computer may appear to be frozen on the Apple boot picker menu so give Knoppix lots of time to boot especially if the internal drive may be bad.
If Knoppix boots to the desktop, then click on the "Start" menu in the lower left corner of the Taskbar and navigate the menu to "System Tools ---> GSmartControl". Within the GSmartControl app double-click on the Mini's hard drive to open up its health report. Post the complete report here so I can examine it. If you have more than one internal drive, then make sure to post a report for both drives.
If you have trouble creating a bootable Knoppix USB drive then let me know.