Hoo boy, how this can happen is a good one.
You're saying that when you set the Air and Temp controls to "Heat" and the Def control to "Room" you get cold air on the driver's side foot control area and warm air on the passenger's foot area.
I am gathering this from your statement that both of the small doors for the floor are open, and the only way those open is when you put the Def control to "Room". Additionally in order to get heat at all, you must have both the Air and Temp set to "Heat".
If this is correct, I would say that your heater core is plugged inside, and you may need to replace it or have it taken to a radiator shop and have it boiled to get all the gunk out of it.
See the heater core is like a miniature radiator, and the hoses to fill / drain the coolant from the engine are on the passenger side of the core. The air that exits out the little doors enters from above the core and is forced through the core to gain heat and is then expelled out those little doors. Since you are feeling heat on the passenger side, but not on the driver's then the "lower" or driver's side of the core must be plugged and not have coolant flowing through that part of the core, hence, no heat on that half.
You MAY be able to use one of those radiator flush solutions and it MAY fix the problem, but since those solutions are basically various forms of acid(s), you MAY find yourself opening up a HUGE can of worms. Ruptured hoses, seals, and other problems may ensue.
The other possibility, although far fetched, is that your heater control valve is opening up only a little bit and what hot water is entering is being cooled down as it first enters such that your side of the core doesn't get any warm coolant at all.
In either case, I would first check the heater control valve, make sure it's opening up all the way, then check the heater core. By the way, although messy the best way to check the heater control valve is to remove it out of the car and actuate it manually. When you go remove it, remove the carpeting and padding from the passenger foot well and then get a couple wine bottle corks to plug the hoses once you've removed them from the valve, then proceed. OH, and don't forget, put lots (LOTS) of rags below where you will be working to catch that anti-freeze stuff. It's notorious for staying damp for weeks, and you don't want it getting on your floor boards.
My 2¢ worth.