"Darkened" is the past participle of the word "dark," a participle being the "ed" or "ing" form of a verb. In the example you give, "darkened" functions as an adjective and indicates the tense of the word "dark." This shows how it functions in time: the room used to be light but, over a period of time, became dark. In the second example, the room is simply characterized as dark. "Dark" in that sense is used simply as an adjective to describe the room.

Darken: something that you can control--->you can choose to CLOSE the light to make the room darker/dimmer. Dark: something that is natural--->it's (naturally) dark inside the room, whether outside is day or night; however, you can still bring a flashlight/lights/etc.

To darken means "to make something dark" or "to become dark". This might make the difference clearer.