(a)Maybe things have changed over the past couple of years but so far as I know transparency isn't bakeable yet so the screen area will need special handling.
(b)At the back of the model, the part with the material named "Frame(Backside).001" and the part with material "Back Cover.001" are nearly overlapping.
That overlap is bad for any type of rendering because the floating point precision limit makes it difficult for the renderer to know exactly where both parts are in relation to one another because both parts are essentially in exactly the same place once numerical imprecision is considered.
You can get away way with using close flat polys for a camera render if the model and camera are close to the grid center and to each other but still; super close, parts flat parts should be avoided.
This type of error is called z-fighting.
And I believe it's why the those parts are coming out black when baked. They overlap and so both are being baked as if they are each inside the model and hidden from the light. The baker can't tell which one is outside and which one is inside where it's dark.
I think the overlapping geometry also causes BVH(bounding volume hierarchy) build issues since Blender froze on me when I tried to bake the model. BVH is a spatial partitioning optimization technique.
I forced Blender to shutdown and then my OS crashed. Bluescreen of death. The freezing of Blender took place right at the beginning which is when the BVH build takes place.
Anyways, once I separated all the parts and moved them to their own layers and baked them one at a time to look for issues, the BVH freezing no longer happened and everything baked with lighting applied properly. There were no black parts showing up in the bake. There were some errors on one of the pieces but that looked like a UV-mapping error and I didn't try to track it down. That's a separate topic and this is all long enough already.
(i)You can either baked all the parts to their own textures as in Diffuse_0.png, Diffuse_1.png, Diffuse_2.png, etc, and then combine them all in a 2D photo editor like Krita, GIMP, or PS. using part masks or...
(ii)You can also UV-Unwrap models with complex pieces as separate parts right from the beginning of the process so they can easily isolated and baked. Once all the pieces are baked, you can then join them and and create a second UVMap. Now set all the materials to be Emission shaders which acts as a simple image color passthrough and then bake the pieces all to one final UVMap set like what you have in your model now.
You made things too complicated by trying to bake nine materials, a model with hidden parts, multiple types of shaders(Diffuse, Glossy, Emission, Transparency) all at the same time.
And since you can't bake transparency(so far as I know) you have to handle the screen manually after everything is baked.
(a)You can either bake an alpha mask(transparency mask) or use the rectangle tool in a 2D editor to select the screen portion of the image and make that area transparent.
(b)To bake an alpha mask, use a temporary Emission shader that can mix between black and white and apply that material to the entire model. Set anything opaque to be white and the screen to be black.
Now in a 2D editor, this baked transparency mask can be pasted into the alpha channel.
On a side note, that large back piece that is hidden inside is just a waste of uv-map space, it should be deleted.