Reinstalling MacOS Sierra on a Mac Book Air, screen unresponsive for hours

See if this helps:

Install El Capitan or Later from Scratch

If possible back up your files.

1. Restart the computer. Immediately, at or before the chime hold down the Command and R keys until the Apple logo appears. When the Utility Menu appears:
2. Select Disk Utility from the Utility Menu and click on the Continue button.
3. When Disk Utility loads select the volume (indented entry, usually Macintosh HD) from the Device list.
4. Click on the Erase icon in Disk Utility's main window. A panel will drop down.
5. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
6. Click on the Apply button, then wait for the Done button to activate and click on it.
7. Quit Disk Utility and return to the Utility Menu.
8. Select Install OS X and click on the Continue button.

If you cannot boot from the Recovery HD, then you will need to try the following, but it will only work on models that came with Lion or later pre-installed - no Software Recovery DVDs.

Internet/Network Recovery of El Capitan or Later on a Clean Disk

1. Restart the computer. Immediately after the chime hold down the (Command-Option-Shift-R) keys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the target drive (will be the out-dented entry) from the side list.
5. Click on the Erase tab in Disk Utility's main window. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
8. Click on the Apply button, then click on the Done button when it activates.
9. Quit Disk Utility and return to the Utility Menu.
10. Select Install OS X and click on the Continue button.

This should install the version of macOS that was pre-installed on the computer.

I would keep trying to shut it down, but if you are not successful then make an appointment at the Apple Genius Bar for service. If you need to find an Apple Store - Find a Store - Apple. Also, see How to find your nearest Apple Authorized Service Provider (AASP) or Distributor (AAD).

If you disconnect the charger, then it will shut down once the battery goes dead.