What kind of damp do we have?
Very interesting situation.  First off, replacing perfectly good vinyl windows is not going to help you from what I see on your pics. Simple weeping drains around windows is not going to help much with all the moisture I see on walls, ceilings and floor.

I would suggest you have someone come in with an infrared scanner and make a sweep of the building to determine areas where moisture may be coming from. If the water is coming in from outside through the roof, floor etc., infrared should be able to see it. knowing where the sources of moisture are will help you in making decisions on how to mitigate it.

If this problem is internal condensation, you may need to install some sort of ventilation system. Dehumidifiers certainly would help, but depending on the areas in the house creating the problem may be addressed with better ventilation.  Bathrooms, laundry are prime areas for excess moisture.

Since this condition is creating mildew and mold (seen in pics) , I think you should have some professional evaluation before the mold situation becomes a serious health issue.