What I have:
So I have a class with a private member, and a static function. The function must really be static and I can\'t change that.
You can't. You need an instance to get to the non-static private. In the static method you don't have an instance available.
So you need some way to get an instance, either by passing it to the static method, or by being able to get it from somewhere else. But in that case, you could as well make it a non-static method.