Here's the outside of the fixture. The rectangular switch is supposed to go up and down, switching the lights on and off. It no longer does.

This morning I decided it would be easy enough to replace it, so I unscrewed the fixture from the wall. Hmm. Looks like it might be more difficult than I thought as the wires appear to be soldered onto the circuit board (guess that's what it is) on one end, and somehow permanently attached on the other.

Any ideas? As you can probably tell, I'm EXTREMELY mechanically minded.