Is there a way to measure it electrically if the humbucker is ok or broken? Like resistance? If so, what is the resistance if it's ok or crap? A basic device for measuring resistance (and maybe few other electric units) doesn't cost very much in a hardware store. I'm just not the one person to say if it can help you with this problem or not.. 😡
If the humbucker is broken, you might just want to take advantage of the situation and replace it with a better one. Often used are DiMarzio, e.g. Super Distortion, or Seymour Duncan (e.g. JB), but you should of course think it through yourself; what do you want from the humbucker.
Of course it's annoying if you buy stuff and it's already broken, but if there's only one broken pickup and the rest of the guitar is intact, the best way to cope with it is probably to fix it.