Try these steps:
If you actually instead have the newer Google Nest Mini (2nd gen), at step 3, you will need to press the mute button on the back for at least 15 seconds and then it will reset.
Are you using the original power supply and adapter that came with it? You mentioned having tried a normal factory reset (the steps I shared above are a more advanced reset). Did you follow the exact steps below?
On the bottom of speaker, press and hold the factory reset button located below the power cord. Look for a circle etched into the base. After 5 seconds, your device will begin the factory reset process. Continue to hold for about 10 seconds more, until a sound confirms that the device is resetting.
If you actually have the 2nd gen model, you'll need to switch the mic off using the switch on the side of the speaker. The lights will turn orange. Then press and hold the center of the Nest Mini, where the lights are on top. After 5 seconds, your device will begin the factory reset process. Continue to hold for about 10 seconds more, until a sound confirms that the device is resetting.
You might also want to try plugging your speaker into a different power outlet just to test.
Chiming in, since we have exhausted the troubleshooting steps, the next thing to do is to replace your device. However, as much as we'd love to replace your device, it's no longer within our Limited Warranty. We know this is not the best answer that you're looking for, but let us know if you still have other questions otherwise, I'll be locking this after 24 hours.
Thanks for the reply. We regret to tell you that since your device is already out of warranty, we can no longer replace it. You might want to check this link for more info about our device's warranty.