Likely cause is a broken seal which could have been sealed to stop moisture intrusion to this extent and avoided window replacement.

I don't see major issues during a quick walk through but wanted to get your opinion as it seems there are a few cracks on both sides of the house denoting signs of settling/moisture/etc. and some crumbling (pictures below)?  

If a spot appears wet there is equipment called a moisture meter that reads how wet currently the area is.

I know flagstone has issues with moisture over time, hence it starting to slant or slope.

If you want carpet, go with a super cheap frieze and get a good quality pad with a moisture barrier (8lb pad).

I wanted to get the opinions of all the smart people on this forum on whether the rest of the stained drywall really ought to be removed (to prevent further problems, e.g. mold), or if it would suffice to just to let it sit for a little bit longer (i.e. to make sure any possible moisture is dried out)  before applying kilz and painting over it.

Another concern is water penetration, so you want to see what happens after a rain storm. 

We have a problem with too much moisture in our home and the condensation build up in the winter is rotting the skylights wooden frame. 

I truly can only assume where the moisture is coming from.

We prefer forced air heat/cooling as the air movement provides even heat and helps prevent moisture problems.