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Unfortunately if the partition for Windows 8.1 recovery image is gone we don't have another one to provide and the system cannot be recovered.
At this point if the partition for Windows 8.1 is still available I would suggest the following:
Update the Intel® Compute Stick BIOS; please download the latest BIOS version for this unit at:
https://downloadcenter.intel.com/download/25506/BIOS-Update-FCBYT10H-86A- Download BIOS Update [FCBYT10H.86A]
In this case I recommend doing a BIOS recovery and you can follow the steps at:
http://www.intel.com/content/www/us/en/support/boards-and-kits/intel-compute-stick/000005902.html Intel® Compute Stick BIOS Recovery Instructions
After that is done reset the system to factory defaults:
If this troubleshooting work for you try upgrading to Windows 10 again, please follow the steps to upgrade to Windows 10 at the following link:
http://www.intel.com/support/motherboards/desktop/stck1a32wfc/sb/CS-035724.htm Intel® Compute Stick STCK1A32WFC — Windows® 10 Upgrade Instructions