I took a Williams unit apart a while back because it wasn't working. Turned out to have a burned out (and badly melted) coil.
While swapping out a coil is easy, doing anything else with a play counter is not. They're a nuisance to disassemble and reassemble, and as others have pointed out, you can pick up a used working one for about $10 on eBay, which, as it happens, is what I had to spend to buy a new coil.
You could probably fix it, but for me, this falls into that "life's too short to spend much time on this" category.
My 2¢. YMMV.