Water intrusion is almost certainly caused by improper (or total lack thereof) flashing on top horizontal portion of exterior of window. Improper installation along with no caulking is other culprit.
Get on ladder outside and start poking around. I'm guessing you'll find your problem in short order.
I was investigating a bit more yesterday evening and cut some inspection holes (forgot pics) however, the "extended sill" runs underneath the window to the outside. I was able to take a small carpenters square and from the inside, run it under the window and hit the vertical section of the flashing on the outside. Not to mention could feel all the cold air rushing under the window and into the wall gaps. Which explains why the walls are always so cold.
So the caulking on the horizontal part of the exterior flashing has broken down or was shoddily applied leaving gaps which allowed water to come in, hit the drywall, and compromise it so that it would eventually sag, allowing more to come under when the seal between the drywall and the bottom of the window failed.
In one of the holes I cut I can see one side of the "framing" for the window. Or atleast I assume thats what it is. THe joint where the bottom meets the side as separated. I can see the rusty nail that went in through the bottom. Assuming moisture has started rusting it away and it lost its hold. Can also see damp spots on the plywood below for the floor below that area.
Just a big mess in general. I'll take some pics of what I've found and post them this evening. Probably won't cut more out as its going to be in the teens tonight and trying to keep out as much as possible.
