Are you sure the plumbing is done correctly? Maybe you are drawing hot water only from a furnace (or boiler) tankless coil and the stand alone water heater in the crawl space is not sending any water anywhere. THen when the furnace quits, no hot water.
Tornado victims: Do not rush to rebuild. Take your time and look for and get a good contractor. Or consider selling the property and moving to a home that is ready to live in.
I looked up the "furnace" model number, and it's actually a boiler. So if you have a domestic hot water coil in the boiler providing your hot water, that would explain why you get no hot water when the boiler pilot is out.