Extrapolating from what you've written; mini has been unplugged (to get out of freeze). You're not getting a caps lock on trying to start up.
Q: is this a wired keyboard or wireless?
Q: where does it freeze up on starting up? at the Apple logo or ... ?
Q: have you tried recovery mode? (link: [
support.apple.com]) & below)
Q: barring the above, have you tried internet recovery mode?
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Start up your Intel-based Mac in macOS Recovery
Restart your Mac.
Immediately press and hold one of the following key combinations until you see the startup screen:
Command-R: Start up from the built-in macOS Recovery System. Use this key combination to reinstall the latest macOS that was installed on your system, or to use the other apps in macOS Recovery.
Option-Command-R: Start up from macOS Recovery over the internet. Use this key combination to reinstall macOS and upgrade to the latest version of macOS that’s compatible with your Mac.
Option-Shift-Command-R: Start up from macOS Recovery over the internet. Use this key combination to reinstall the version of macOS that came with your Mac or the closest version that’s still available.
If you see a lock, enter the password for your Mac.
If you have multiple volumes on your disk, select the volume you want to recover, then click Next.
If requested, choose an administrator account, click Next, enter the password for the account, then click Continue.
When the Recovery app appears in the menu bar, you can choose any of the available options in the window or the menu bar.