If the TV module was that corroded, then replace it. - I think it was corrosion, it was covered in a white powdery/chalky substance.

And fix the source of water entry into the vehicle! - Is there any easy way to trace the problem? Is it a known issue?

To make the nav work without TV, you'll have to join the video lines together in the blue and white TV module connectors. - Is there a connector I can get to go in between the blue and white connectors or do I need to take the connectors off and join cables manually?