First of all, there is nothing in the tank that would have anything to do with your problem. I suspect something is lodged in the trap. True, toys are frequently the culprits, but other things can accidentally end up being flushed. There is a tool call a Closet Auger that can help snag obstructions. Sometimes you have to pull the toilet up and go at the problem from the underside and push the object out the way it came in. There's no one method that works every time. Since this is not your home, I would suggest the wise thing to do is call a plumber. This will avoid having to explain damage to the bathroom and/or toilet to the owners. If it was your own home, then you could accept the risks involved, but I do not think it would be wise to do more than pretty much what you have already done.