Again (wishing I had my PHB here to quote). The only reference to immunities in PHB is p55 under the heading Keywords. I know this because I searched my PDF version thereof. There is only one sentence there about immunity and it has been quoted many times in this thread already. Immediately following the line about immunity it tells you how to resolve damage with multiple keywords by splitting the damage among the keywords. Unless there is a rules reference somewhere else I am unaware of (other than PHB3).
This is the problem:
You are confusing 'damage types' with 'keywords.' They are not the same thing, in the same way an implement is not the same thing as the Implement keyword, the Beast Form is not the same thing as the Beast Form keyword, and a Spirit companion is not the same thing as the Spirit keyword.
Are they all related? Yes. The keyword indicates there is a relation, with varying rules to determine how they relate. But the keyword and the game element they relate to are not the same thing.
The same thing occurs with keywords relating to damage, and damage types. Take, for instance:
Blazing Starfall - Sorcerer Attack 1
At-Will - Arcane, Fire, Implement, Radiant, Zone
Standard Action - Area burst 1 within 10 squares
Target: Each creature in burst
Attack: Charisma vs. Reflex
Hit: 1d4 + Charisma modifier radiant damage.
Level 21: 2d4 + Charisma modifier radiant damage.
Cosmic Magic: The burst creates a zone bounded by
burning ground that lasts until the end of your next turn.
Whenever an enemy within the zone leaves it, that
enemy takes fire damage equal to your Strength modifier.
Let's assume for sake of argument you are not a Cosmic sorcerer. This being your only Area at-will option, you might take it anyways because an Area at-will is good in the hands of -any- sorcerer.
The power only deals radiant damage. Ever. It can never deal a single point of fire damage.
HOWEVER
The effects of the power are still Fire effects, because the power has that keyword. The radiant damage? A fire effect. Also, a zone effect, an arcane effect, and an implement effect.
Abilities that interact with such effects will interact with ALL those effects regardless of the fact that all the power can do is a burst of radiant damage.
In the PHB, immunity states you cannot take damage from foo effects, and that is why someone immune to fire (pre-PHB3) would never take damage from this power. The entirety of it is a Fire effect. It just doesn't deal fire damage.
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Damage does not have a keyword, it has a damage type. If you do '4 fire damage' that is not '4 damage with the fire keyword.' Keywords are things powers have, and all effects of a power share that keyword.