stepping on the colored lights (in the proper order) allows you to open the door to the room where the pedetal for the capstone is and also the black chest. There is no other place to put the capstone except there (and where the writ of fate appears when you place the capstone) and you must walk the star in the correct color order in order to open that door.You said you have placed the capstone and have the writ of fate, so you have been in there.
I can't understand how you got the door to open without walking the star correctly.
There is another set of double doors in there that I have never been able to open, but they have nothing to do with winning orlosing the game and the pentegram also has nothing to do with them (I don't think).