Welcome to the monkey house! AND, many thanks for providing pics -- they really help in giving you quick and more accurate advise.
1. Looks like some nasty water damage ... was this from the old window or since the new one has been installed? If it happened SINCE the new window, your exterior flashing and sealing is bad. You need to remove the window and fix that. Then you need to sand, prime and paint the window stool (most people say "sill"). Then you need to properly re-install the window with sealant, insulation in the voids and trim molding.
2. If the damage was pre-existing and the window is not leaking then great! However, I see no floam sealant around the window and no insulation in the voids. Add that to the window. Clean up the stains, prime and paint, install trim mold, throw a garage party!
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