Ok. I've made no progress with this at all and I'm pretty stumped. I've searched high and low for a valve or something, but I have found nothing that will make the faucets work.
Maybe some pictures will help?
This is what I'm looking at. Heat exchange which feeds the faucets:
Following the lines to the left a little:
And the controls for the heat exchange outside:
That's kinda all I've got to go on. The only thing I haven't done is filled the fresh water holding tank. Is it possible that the faucets would only work off that?
Again the shower and toilet work just fine as is.