Help! My Hatsan BT65 (and other models) does not cycle anymore!

You're ready for an afternoon of shooting. Everything is ready: The rifle is pressurized, the bullet trap has a card with a brand new taget, and the magazines are filled with your favorite ammunition.
But then! You are ready to shoot, you suddenly find out that the rifle does not want to cycle at all!

This can of course have a thousand and one causes, but today we are going to discuss (and solve) the 2 most common ones: The barrel o-ring and the magazine rotation.