Well, maybe you could inspect the plumbing near the leak for any cracks, etc., but if you can't find anything you are going to have to turn the water on to find the leak. Its already been wet so I guess a little more water won't do any more damage provided you can dry it out once you find the leak.
Does your thermostat control the AC or only the heater? If only the heater, try shorting the 2 wires to see if the heater comes on. If it also controls the AC, I don't know which of the wires control the heater.
I'm no expert, especially on the heater, so there is not much I can help you with. But I thought I would try.