Reducing Render Times for Cycles Animation Rendering via Light Baking?

Hello Blenderartists Community!

I have picked up Blender 4 weeks ago and have not been able to put it down since then.
I have kind of hit a dead end with the cycles render engine now because the render times have started to explode.

Here is my current project:
I am trying to create a very simple animation of a few moving objects which are part of a bigger, static model which doesnt move during the animation at all (it’s simple animation stuff like some screws turning and moving).
Render Times have exploded because in Order for Cycles to not be grainy I need around ~800-1000 passes + I wanted to render it in 1920x1080 Full HD Quality. 1 Frame takes around 20 minutes to render and I have like 160 of them which makes waiting not an option in my opinion.

I was thinking that the perfect solution would be baking the light beforehand since 95% of the model does not move at all during the animation! The only thing that moves are very small individual parts which are not part of the main thing + the camera.

I followed this tutorial and the light baking worked like a charm. What a neat tool!

Here is my question though. When I tell Blender to render now, how does it actually know it doesn’t have to render the 95% of the object with the baked textures on it but rather only the parts which actually move?
In the testing environment I created where I baked every single texture and hit “Render” it took 8 minutes even though everything was baked onto the model (Full HD and 1024 passes).
I would like to ask if you could tell me where exactly I went wrong here.

Sorry for my first post in this community being a question but I tried googling and youtubing the solution and nothing came up.

Cycles seems to figure that out on the fly since you can see the tiles speed up when rendering a baked material. Did you turn the lights off not needed anymore. Also try rendering on the CPU since it could be a GPU thing. And, finally you got from 20 to 8 minutes guy.