I'm making a map, and part of it utilizes the sky.
Meaning, a skybox.
Thing is, this light source, in each room it is present in, is supposed to start blocked out by a hatch in the ceiling. Said hatch is made of func_doors. But, the light shines right through them.
I've tried my best to remedy this issue, like temporary func_brushes with the BLOCK LIGHT texture, or any other texture, and trying to use other brush entities to block the light to no avail.

If someone can help me here, it would be greatly appreciated.
And if it's impossible, I'm very disappointed.

If you don't already have an env_projectedteture in your map, that may work. If you have multiple holes in the ceiling, it may be weird to work with, given that only one can be on t a time. Try placing it in the hole with the desired angle. The thing about the light source you may be using is that it probably can't support dynamic shadows. The env_projectedtexture is capable of doing dynamic shadows, and therefore would look real good in your scene. If you already have one on, try placing a light_dynamic. It's shadows are crappier, but it should work(ish) in the end.

Here is a tutorial by the brilliant tophattwaffle:

http://m.youtube.com/watch?v=tTq-hRyxCZU

Mmm, well, I did an experiment with light entities, and it seems that no matter what light entity I used, it would pass through the brushes beneath it.

Yes, most light in the Source SDK is static (baked into the map). As Arachno said, you need an env_projectedtexture for nice dynamic shadows.

Be sure to have Enable Shadows on and the flag Always Update checked