problem starting Mac mini from sleep mode

If the light on the front of the Mac mini is on..?

Hold the power button for 10 seconds or until the Mac mini shuts off.

Then wait for 30 seconds and push the power button to turn it on.

If the light on the front of the Mac mini is not on..?

Check the power cord on the back of the Mac mini.

Then check where the cord plugs into the wall outlet and/or surge protector.

If that does not help, work thru the steps at > If your Mac doesn't turn on - Apple Support

For additionally help, please identify the year model of the Mac mini and macOS version.

see > Identify your Mac mini model - Apple Support

First try den.thed's advice & if you get it started then...

Are you running any VPN, Anti-Virus, or Cleaning apps?

We need to see what all is running, a report from this will not display any personal info...

Using EtreCheck - Apple Community

EtreCheck is a FREE simple little diagnostic tool to display the important details of your system configuration and allow you to copy that information to the Clipboard. It is meant to be used with Apple Support Communities to help people help you with your Mac. It will not display any personal info. Give it Full Disk Access.

https://www.etrecheck.com/

Give etrecheck Full Disk Access before running.

Thanks for Old Toad’s etrecheck instructions…

Slow iMac 2017 - Apple Community