Turn on the power:
In the power room, you need to use one of the consoles to program in a sequence using the coloured shapes that directs the repair drone to the lens (which is lying on the floor), picks it up, then places it into the pinnacle that is missing its lens. I can't remember the actual sequence, but it's more fun to work it out for yourself, anyway. The second console activates the repair drone. Once the power is activated, you will be able to open the doors.
If you don't know how to open the doors:
The coloured rods that you pick up here and there have the key to the door of the matching colour. Enter the sequence of shapes that you find on the rods (examine them) into the consoles by the appropriate door.
Hope this helps!