It seems like this was the way it worked originally, but someone had it changed. There is another area in my apartment that is in the same situation. I measured 114VAC from the right switch (I'm assuming the fan) and 86VAC from the left (not sure what's connected there since it does nothing). Please help!
86 volts sounds like you might have an open neutral, and you're reading backfeed through a load somewhere. Time to call an electrician - usually this sort of thing happens because a white wire on 2 conductor cable had been used for a switch leg, but somebody went into a box and went color to color putting wires back together, which opens the normal return leg for current. It could be the box pictured, or your ceiling box for the fan/light, or something you haven't looked at yet. A tone tracer [breaker off] and some detective work will find it - the last thing messed with is the first place to look. Meanwhile, make a note of everything that does not work to help out: lights and receptacles. Plug in a cell phone charger or whatever to outlets to see if they're good. Open neutrals can be a rattlesnake for the unexperienced: just because something doesn't work does not mean it can't shock you.