I'm afraid I don't know how to help you
So you can't even jump?
If you jump into a wall it automatically clings to it
Do you have the climb ability from the shop?
To do what?
Are you on console or PC?
Have you tried restarting the game or your console PC?
It is impossible to reach the end crefits without opening the Cabinet. New game + is irrelevant.
@Ionut Faur just play the game my friend and you'll find out.
Achievement earned: Be Lectured on Happiness