If there are no villain ongoing cards in play, but you have damage boosters (Inspiring Presence, Staff of Ra, Imbue Fire, etc.) does this power still deal damage? Essentially, does 0 + 1 = 1? Or does there need to be at least one ongoing card for this to work?
I would say it still works. Just like if 1 damage is reduced to 0 by Voss but increased to 1 by Galvanize. Although it temporarily became 0 but it’s the final number that counts.
Really this is almost the same question as Brain Burn. What he is asking is if having no ongoing cards in play count as no damage at all (and no damage can’t be increased because there is no damage to increase) or if the damage is combined as a single point of damage (which would be zero damage, increased to whatever amount).
Basically, if you’d play three ongoing cards as giving a total of six points of damage when increased by one, then zero ongoing cards results in no damage; if you’d play three ongoing cards as giving a total of four points of damage when increased by one, then the zero ongoing cards would result in one damage. The same effect would then consistently have to be used for non-hero cards that do the same, such as Pterodactyl Theif.
I was less interested in exactly how the damage would scale from boosting than whether or not it worked with a base of 0, but yeah, you’re correct, it’s worded the same as Brain Burn.
In case anyone cares, the reason we wanted to know is because we were playing against The Matriarch, who never has ongoing cards, and we wanted to know if Legacy’s Galvanize would be enough to allow Ra to take out Fowl with Drawn to the Flame 
If a card does x damage where x is... it does one instance of damage. if a card does 1 damage for ... it is many instances?
I'm having trouble understanding your question. do you want to try rephrasing it?
Yes.
To use examples in the cards, Visionary's Brain Burn does X damage, where X is the number of cards removed from the villain trash. So if 3 cards were removed, she deals herself 1 instance of 3 damage. Tempest's Vicious Cyclone deals 1 projectile damage for each card discarded. If he discards three cards, he will deal 1 damage 3 times, each one being a separate instance of damage.
I thought that brain burn did many instances?
Not in Enhanced Edition.