The 'correct' way of cooling stock is to put the stock-pot in an ice-bath or in the sink with running water. If you put it in the sink, you don't even have to open the tap too much. Just a little stream of water is enough to cool the stock to room temperature in about half an hour or so. Then you can put it in the fridge.
A stock that's been left on the sink for more than 4 hours at 24ºC is a health hazard. You should take the stock at your own risk.
Harold McGee wrote and article on this very topic and the short answer seems to be that while you're not 100% safe with your stock, you could risk using it after a 10 minute boil:
I’ll admit to violating the guidelines in my own stock-making, though by a few hours, not days. When I cook a roast for dinner, I use leftover scraps and bones to start the stock, simmer it while I clean up, and take the pot off the heat right before I go to bed. At that point it’s too much trouble to cool the hot stock so it won’t warm up its neighbors in the refrigerator. Instead, I cover the pot, leave it at room temperature and reheat it in the morning, about eight hours later, before straining, cooling and refrigerating it. And my stock hasn’t made me or my family ill, either.
What about my lazy method of letting stock cool overnight, then reboiling and refrigerating it first thing in the morning? Dr. Snyder gave it a pass because it would spend only a few hours below 135 degrees, not enough time for the bacterial spores to germinate, start growing and reach hazardous numbers.
Any active bacteria are killed by holding the stock for a minute at 150 degrees or above, and botulism toxin is inactivated by 10 minutes at the boil.
The whole article is very interesting and worth reading in full.