Thanks for reaching out. Oh no! I am sorry to hear that your Google Nest Mini is not powering on. I understand your concern and would be more than happy to help find a solution.
First, could you try this troubleshooting step?
After plugging in the power cord back in the final time, wait a few moments for the device to reset. It will announce "Welcome to Google Home" to signify that it's ready for setup.
Please let me know if this helps resolve the issue or not. I look forward to your response.