Annoying when this happens at a live gig. I feel your
Have you tried to replicate the problem at home & do you still get no signal?
So you're down to a process of elimination.
Firstly, I'd remove the batt box & try the mics straight into the Tascam's mic input. First make sure Plug-in-power is switched on in the recording menu. (I think that's where the option is, but I don't have a DR05 to test) You won't get such a large dynamic range, but the mics should work fine for testing with speech.
Then, if there's still no joy, unplug your CA mics and try the Tascam with its own internal mics.
I think this Tascam auto-switches to internal mics when the external plug is removed, so there should be no settings to change & it should just work.
Surely you'll get something now...