Hi rich,
the short answer to your conundrum for the A320 is: you need hydraulic pressure to fly the aircraft. Period.
I see two possibilities in the case you postulate:
1. get the RAT to extend by pushing the electrical or hydraulic panel manual extension buttons
2. start the APU (provided the aircraft is within the start envelope, otherwise you would waste valuable battery power, but in my opinion, you would try anyway....)
The screens going blank on battery power alone are the least of your worries in that case (one is left with Capt PFD and ND on battery).
Cheers Rapide