Paint on the reflector should not be an issue as long as the paint is scraped off under the screw heads to ensure good contact with the fixture.
So that's what this problem boils down to. What an easy fix.
Update: I tried turning it on again, and it's broken again. But to fix it, I scratched some paint off where the screws are, and it finally turned on again. It works!
I guess it's a case of persnickety screws.