Basically, can Dooku trigger his ability if he has shields that block all incoming damage?

Based on the ruling for Hunker Down, I would say No.

Hunker Down (164)

If shields block all melee damage that is dealt to a character with Hunker Down attached, the character did not take any damage and keeps the upgrade.

Count Dooku:

Before this character is dealt 1 or more damage, you may discard a card from your hand to give him 1 shield.

Scratch that: Looks to be "Yes" after double checking and realizing his text talks about damage dealt and not damage taken as in Hunker Down.

Taking Damage:

Damage not taken is still dealt .

Yes "Damage not taken is still dealt".

Yes "Damage not taken is still dealt".

This. Hunker Down requires that you take damage, Dooku requires that damage be dealt to him. Two different things.

One important thing to note is that if Dooku already has three shields and is dealt one damage, he won't be able to use his ability and will stay at three before taking damage.

I had an opponent at three shields on Dooku. I dealt 1 point of damage. He thought he could burn the damage with a shield AND use Dooku's ability to stay at three shields. Nope. Timing doesn't allow it.

And if I understand it correctly, he could use this more than once during a single damage resolution action, correct? Like if an opponent had a 1-range die AND a 2-range die to resolve during the same action, Dooku could discard one card against one die, then another card against the second die. Correct? (Since each die, although part of the same action, is resolved separately).

Fromm p15 of the RRG:

••Damage dealt during the same action is usually dealt at
different times since the dice are resolved one at a time.
The only time multiple dice deal damage at the exact same
time is when a die is being modified by other dice.

Yes

Kewl thanks.

That's why against Dooku it's awesome to get a 3 damage and a modifier +2 and hit him big, he can only reduce it once

You can use Dooku's ability once per source of damage. So a 1 Ranged and a 2 Ranged, which are resolved separately, would allow Dooku to use his ability twice. But a 1 Ranged and a +2 Ranged Modifier makes for one source of 3 damage, and Dooku could only use his ability once against it.

On 11/30/2016 at 1:58 PM, KrisWall said:

One important thing to note is that if Dooku already has three shields and is dealt one damage, he won't be able to use his ability and will stay at three before taking damage.

I had an opponent at three shields on Dooku. I dealt 1 point of damage. He thought he could burn the damage with a shield AND use Dooku's ability to stay at three shields. Nope. Timing doesn't allow it.

Well it is important to note that they can still use Dooku's ability to discard and gain a shield it just goes away before taking the damage. So not sure why you would do that unless you needed to get rid of a card for something like mindprobe.

18 hours ago, gamer1886 said:

Well it is important to note that they can still use Dooku's ability to discard and gain a shield it just goes away before taking the damage. So not sure why you would do that unless you needed to get rid of a card for something like mindprobe.

While that will help against future mind probe specials, if Dooku is currently being dealt damage from mind probe, discarding for his ability will not change the damage for that action. His shield will reduce it, but his hand size was already checked before he had a chance to discard a card.