MacBook Air dead dead after high Sierra update

Well, which MacBook is this (year and model)? What version of macOS was running when you started to try the Catalina and High Sierra update/upgrade?

Well, definitely let it charge all the way up and then have plugged into AC if possible before trying to do a Recovery style boot (hold down command+r during power on), if it will power on. But since the system was on and very active doing the install when you lost power, might have totally corrupted the disk. Do you have any backups of system before you started the update attempt? You might need to completely erase the disk. Did you have or did you already get the High Sierra installer or Catalina installer app and possibly create a USB type installer? Or do you have the High Sierra update with the "dmg" file that contains a "pkg" file when you mount the dmg file and then run that?

There is more than one type of Recovery boot -- command+r is normal recovery that lets you reinstall the latest macOS that was installed on you MacBook, command+option+r lets you upgrade to the latest macOS that is compatible with your MacBook and command+option+shift+r lets you reinstall the macOS that came with your MacBook when it was new or the closest version still available. Take a look at this page for more instructions: https://support.apple.com/en-us/HT204904

Good luck..

Several of your keyboard sequences are unknown to me (fn-control-command does what?). So please make double sure of what you're pressing during boot up. Caps lock does nothing as far as I know.

The control-shift-option (must be the ones on the left side of keyboard i think) + ON is an SMC reset for MacBook Air I think, so would think this would clear up any bluetooth keyboard pair information but am not certain of this, but if not then you can open System Preferences and then go to Bluetooth and then remove the wireless keyboard if you can get that far anyway.

Try the safe boot -- hold down left shift key during power on -- that will take longer but is more reliable since it clears up caches and does other special things to help clear up problems.

A normal full charge takes several hours on a MacBook air if the battery is OK, so let it charge overnight to be safe, and keep it on the charger while you're doing things cause less problems that way.

Have you tried a Recovery type boot -- hold command+r during start up? If that works, that will let you erase the hard drive completely so you can start all over, which given your situation with it crashing due to loss of power in the middle of the update seems like a good thing to do. But of course, you would need a backup of your old stuff that you can restore from, so perhaps this is not an option for now?

Anyway, wish you the best and hope you get things working.

Good luck...

You probably already figured this out, but just in case... never attempt updates or upgrades on Battery power, generally somewhere between 85% & 50% charge it'll just shut down in the middle of everything.

Do you have a USB keyboard and mouse or can borrow from someone for a simple test - they should work on any Mac I think?

Good luck...