—2011 was the last year Macs shipped with install/restore optical disks. Do you still have those?
—Does holding OPTION during boot change anything?
—Have you tried starting in Safe Mode? Instructions: Start up your Mac in safe mode - Apple Support
If it starts in Safe Mode, let it sit in Safe Mode for up to 30 minutes to allow all the maintenance that Safe Mode does to complete their tasks. Note re the Safe Mode instructions: Use the set under the heading, "If using any other Mac."
—You wrote: "i have not been using my mac mini for a very long time..." Was the computer unplugged from a power source during this time? If so, the little internal battery that preserves settings while the computer is briefing unplugged is surely dead. The battery can protect for a few weeks or months, but not years.
—Crash logs as shown on your screenshot are hard for us mere mortals to interpret, but the pattern I see is similar for those where incompatible RAM was installed. Have you or a d non-Apple service provider added RAM capacity? If so, what make?