... and I can't execute any of the options (F2, F7, F8, F10). I have made a bootable USB stick with Windows 10 Pro, but I can't get the Compute Stick to boot from it - and since I can't change the boot options I am really, really stuck.
Try with a BIOS recovery, see here for the instructions; http://www.intel.com/content/www/us/en/support/boards-and-kits/intel-compute-stick/000005902.html BIOS Recovery Instructions for Intel® Compute Stick, and get the file here https://downloadcenter.intel.com/ Drivers & Software. Remember to filter by your Intel® Compute Stick model.
Could you please confirm the Intel® Compute Stick model you have?
Have tried using a different USB?
Have you tested this USB in a different computer?