Mac mini (2nd generation) Wi-Fi button won't toggle on

What year model is your Mac mini...?

see > Identify your Mac mini model - Apple Support

All of the 2010 thru 2018 Mac mini's have built-in Wireless Wi-Fi chips.

Have you installed any third-party AV, Protecting software or a VPN, that could be blocking the use of Wi-Fi...?

Have you replaced or upgrade the internal drive, if so then perhaps the Wi-Fi chip is damaged or disconnected...?

To setup and test the Wireless Wi-Fi chip in your Mac mini.

see > If your Mac isn't connecting to the internet over Wi-Fi - Apple Support

To run a full hardware test on that Mac mini.

see > Use Apple Diagnostics to test your Mac - Apple Support

Give this a try: boot into Safe Mode according to How to use safe mode on your Mac and test to see if the problem persists. Reboot normally and test again.

NOTE 1: Safe Mode boot can take up to 3 - 5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

NOTE 2:  if you have a wireless keyboard with rechargeable batteries connect it with its charging cable before booting into Safe Mode.  This makes it act as a wired keyboard as will insure a successful boot into Safe Mode.

The Mini has had built-in wireless for about twenty years.

Does it appear in System Information: System Information User Guide for Mac - Apple Support?

Does it appear as an available service in Network Preferences: Change Wi-Fi settings in Network preferences on Mac - Apple Support?

Does Apple Diagnostics reveal any failures: Use Apple Diagnostics to test your Mac?