I don't remember what location you are in. There are R values for certain climates. Let us know about that, and we can help you.

Since you are not going to the outside, wrapping the stud framing surround the window won't work so well. Sorry, I had in my head that you had damage on the outside surround the window.

Get a dehumidifier in that room to help get that dampness out. A fan is helpful too - heading out the direction of a window, but back enough for circulation at the damp area.

Before you paint/ or do any rebuilding - everything has to be very dry. This is where overdoing it is applied. Because water will wick into wood and other material, the outside may feel dry, but there still may be some moisture inside of that material.

It's location has it's own code for where to put the vapor barrier and insulation, and that usually correlates with location/code and climate.

You are right to replace any wet insulation.
You will may want to have your window sill wraped with coated alumin. If you don't have the tools to wrap and bend, it can be a bit difficult, but it's doable. Yes, leaving holes at the bottom slant going to the ext. is important, but you have that already covered.

one the sill has the alumin. Sheeting installed, you should only then caulk the sides of the sill and any area that has an opening to the inside of the window sill. The bottom underside where the sill protrudes out it connects to the siding so that water and cold can't penetrate at that point.

The storm is then left clear of caulking at the bottom so that water can get out. Whether that water is from a device, or from rain/snow.

If you air conditioner leaked into the sill even at a slant, then there could many possibilities for that. The first place I would check is where it is suppose to drain. That area get's clogged by debris and the air conditioner will fill up with water from condensation. I like putting an air conditioner on a platform within a window.

Working today, so will check tonight. Good luck!

I really appreciate your advice. I live in the northeast, in Westchester, NY. In addition to the r-value I would also like your opinion of what substance I should use as the vapor barrier. I am a little short on cash and don't want to go out and buy a huge roll. The wall is only like 10ft by 10 feet with eves that makes it even a smaller area. Could I buy like the painter plastic dropcloths with a high mil thickness. Or is there something special that need to be bought?

Also, the sill seems solid, it looks like the sides are where the gaps are and when the water pooled it ran through the gaps on the side.

your advice is most useful.

Thank you.

you are in New york, and since you are not remodeling everything (meaning the whole wall), it's important to put a vapor barrier around that window and as far as you can go without deconstruction the whole room.

Your insulation should be about R21 value, or just below that, but I do not know what your stud cavity measurement is. Is it 4" or 6"?
You can get faced or unfaced batts and you just measure your height x length and a 10 ft area of a 8 foot ceiling would be only 80 sq. feet. I also don't know what your stud spacing is, but it may be 16 OC. Depending on the age of your home. If you have 4" studs, you need to find an insulation that is only 3.5 inches thick. Does this help you?
The whole idea here, is that you have an older home, and when you use the window unit for cold air at that window, you chances for cold air hitting hot air is more. Older windows in the winter time same thing, just at opposite directions.
Those 6 mil rolls of plastic don't come in little amounts do they? If you cannot afford a huge roll, you may be able to get away with something like a 4 mil, since this is just a small area. I am just trying to get some protection for you around that window.

Do not pack your insulation. The more compact it is, the less it will do for you. In this area, I would just use unfaced insulation, and cover with plastic from the top plate. Down to the bottom Tape/seal any seams or protrutions as well.

Are you going to use sheetrock for a wall material at this location?

Can you get us that pic?