The progress route ended up being bit poorly communicated, so here are some hints for anyone who is stuck:
1. Get the plastic tape, and repair the wires
2. Turn off the gravity module
3. Look at the ceilings of the rooms
4. The spacesuit allows you to go through the hatch, the hatch is the locked door in the room right of the main hall
5. Hatches are to be operated as real hatches (one door has to be closed always)
6. Find the keycode and open the safe
7. Enter the cockpit (the room straight forward from spawn) with the keycard
8. Power up the engines and finish the game.
Hope this helps :D