Heater

That "box" is associated with your mirror but does not penetrate the windshield so it would not be the source of a leak. It may be possible that your windshield gasket has developed a leak at that place. Where are you seeing water? Does it drip down from the overhead console where the courtesy lights are or does it just run down on the inside of the windshield? Your heater problem may be related, but lets first get a fix on where the leak is originating.

It runs down the inside of the windshield

Do you have a sunroof? If not, I would suspect that you have a section of your windshield gasket that is the source of the leak. If you do have a sunroof, It could still be the windshield gasket but I would first make sure the sunroof drains (front corners of the sunroof tray) are clear of any blockages. You can test for this by pouring some water down both drain holes and watching for it to appear on the ground behind the front wheels.