I guess you've tried pushing the button in while cocking the camera, if this doesn't work my guess would be it's something higher up inside the top plate that's the problem. But if you pushed the button in and the frame advance starts to work is the camera back loose on the body? I've had Nikon F's with loose backs and the culprit is the locking tongue that has been bent upwards over the years, it stops the back pulling up snug and while it didn't affect the frame counter on mine the the locking tongue for the back is at the same end of the camera. In fact you could try pushing the back up while winding on and see if this confirms the possibility. If so you just need to bend the tab/tongue downwards with some snipe nosed pliers.