It seems like the dog is the main issue here and not the litter box itself. I would try to keep the dog away from it and see if the cat starts to use it again.
One way, like keshlam suggested is using a litter box that has an entrance the pug can't utilize.
Another option is to move the litter box where the dog physically can't get to it. Maybe up on a bench that the cat can jump on. Another option, since pugs tend to be fat is to get a walk-through baby gate to put on the door to the laundry room and put it in there. It's almost no inconvenience to the humans, the cat can probably squeeze through, assuming it's not fat, too, and the pug shouldn't be able to.
Pugs aren't very athletic either, so you could just get a short one that people could step over and the cat could jump. You wouldn't even necessarily need to section off a room with this approach, though she'll probably be reluctant to go if you just cordon off the litter box and the pug is just on the other side watching her. I wouldn't go the bathroom either, though, if a creepy weirdo was staring at me.
If she refuses to use the litter box, then try to change the configuration and even change the litter to one that smells and feels different. She might have bad associations with the smell and feel of the old one.
Regardless of any of that The cat shouldn't be stuffed into a closet at all, let alone in one with sharp objects. That's a crappy cat owner right there. Why wouldn't they just put her out of their bedroom. Especially, when it's their dogs fault that she's doing all of this. Anyway, give these suggestion a try. Maybe get the pug one of those indoor pee areas if they won't house train it.
