Right. I have finally figured out what the problem was: My keyboard is not a qwerty, and normally when playing wasd-only games I switch my keyboard configuration to British so that they keys are in the right place. However, for this game I switched back to default so that I could actually find the letters I needed to press. Now my default keyboard only has numpad numbers; the numbers on the top bar can only be accessed by holding shift or having caps lock on. This doesn't work in your game: holding down shift or having caps lock on still doesn't make it register. And the number pad didn't work either, as you said.
So the solution I found to play the game was to constantly switch keyboard configuration: default when searching for a letter, then to British when I need a number. If I do this, the game works and I was actually able to finish it (to be fair not having to do backwards jumps makes it a lot easier)