It seems that there has been a little confusion on how to progress from level to level. What you need to do is find the spaceship part for that level and shoot your teleporter beams into it. This is like picking it up and it will teleport you to the next level.

Here is a screencast to get you through while I patch this and make it more understandable in the gameplay.

https://www.screencast.com/t/gOEvqDo1h