I know you wrote that you changed the bulb holder. But the circuit "board" -- actually a flexible "film" with conductive circuits imprinted on it -- is prone to surface corrosion that prevents good contact. Since your other light (the outer bulb) is lit, it's probably not your terminals (to the car's wiring) or the ground (which are shared by all the bulbs).

I would use a pencil eraser, or better some electronics cleaner spray, to clean the foil strips especially where the bulb holder's contacts touch it, and then try again. Checking with a test light or, better, a VOM, couldn't hurt, either, but don't damage the conductive strips with the sharp points of the VOM's probes.

Good luck.