Get a little mechanics mirror (TELESCOPIC EXTENDING INSPECTION MIRROR PLUMBER MECHANIC | eBay) that extends out like a antenna and stick it down into the tank to see if you can spot a failure in the tank. It sounds like to me something inside the tank has either corroded to the point of failure or just flat out failed. The two "****" next to the petcock are for overflow and tank vent. By the way, I think you can find these mechanic mirrors at Autozone for just a few bucks. I just put the ebay link in for the visual.
My last bit of advice is to fill the tank and let it leak. Of course do this in a well ventilated area, but look to see where it stops. This will give you an idea where your problem lies in the tank.