We have a gas furnace/air handler box, housed in our basement, that is leaking water somehow and collecting on the pan and rusting. It has rusted the duct fins and the insulation inside the base of the box is soaked, which tells me this problem currently exists. I have no idea how long it's been going on.

I have a call into an HVAC company to come check on it. Any thoughts?

That water is what is formed when the gas burns and it has strong acids in it which will corrode any metal except stainless steel. You should get a vent that has a way to dispose of that water in the drain since this can cause carbon monoxide poisoning and kill your family. It's a very dangerous situation if it rusts through a pipe or heat exchanger. Get it fixed by a professional.