I just purchased a mini Mac and it doesn’t start

If you have read the "related article" you may have already tried the startup button. Check your power supply, absence of a light on the front of the machine might indicate that a chord might be loose inside that connects the light and any other circuit like an infrared. You do not say what year this is, but, it appears to be an older model from the power plug. The 2021 models are round and the two firewire plugs are not USB-C. Any details you have might give would help.

Not sure, I have a monitor and keyboard. Try the settings on that. If not, enter a new category for using the Mac Book and Mini together on this forum. Tell them the system running on both computers, they may help.

Press the button next to the power cable? Not too brief, not too long. Say 3 seconds.