Blinking folder appears after holding power button

"Blinking folder with? Appears after holding power button down"

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Blinking Folder with a Question Mark:

1. Go Here: If your Mac Starts Up to a Question Mark - Apple Support
2. As it Reads: "A folder with a flashing question mark means that your computer's startup disk is no longer available or doesn't contain a working Mac operating system."

I. Mount > Repair the Disk > Reinstall the macOS::

So, boot in Recovery Mode (Silicon or Intel), and then go into Disk Utility. Select each volume, and see if you need to mount it. Then, select Disk Utility. It will show the word "Unmounted" on the top-right corner of your screen. If mounting is of no success, then use Repair. If that does not work, then reinstall the macOS. If still having issues, then see about getting this serviced. Go Here: If Disk Utility can’t Repair or See your Device - Apple Support

II. So, as For Moving Forward with Getting this Serviced...

A. You Can Take this to an Apple Store:

You'd setup a Genius Bar Appointment at your local Apple Store, taking it in for service. There, it will be diagnosed, and you'll be provided with a cost.

Or...

B. Take this to an AASP:

See an AASP (Apple Authorized Service Provider) in your local area...

Contacting an AASP: 

1. Go Here: Find Locations - Apple Authorized Reseller
2. Click: Service & Support
3. Enter: your location information
4. See: if there is an AASP nearby
5. Contact: an AASP that shows up, and find out more about the services that they offer to fix the battery