Actually, I see a potential point of confusion (indicating my ability to think like a sleep-deprived gamer...):
When you first reach Step IV, the active passive abilities are:
1) Prized 1: If this character is killed or discarded, opponent(s) claims 1 power.
2) If Harrenhal has 3 or more gold on it, discard Harrenhal.
That is, since Harrenhal has not actually been discarded yet, it's "Prized 2: If Harrenhal is killed or discarded, opponent(s) claim 2 power" passive is not active yet. You technically need the passive "discard Harrenhal at 3 gold" to resolve before the location's Prized 2 can initiate.
So if you want to get really nitpicky, the power from the Prized 1 character will be awarded at the same time that Harrenhal is discarded. THEN (and before anything else can happen or any effect can be triggered) the power from the Prized 2 location will be awarded.
The only situation in which this would matter that I can think of, though, is in a Melee game where Player A has 14 power, Player B has 12 power, and Player C kills a Prized 1 character to pay for a Harrenhal with 2 gold on it. Instead of Players A and B both gaining 3 power at the same time (and thus reaching 15 at exactly the same moment for the simultaneous win), Players A and B claim 1 each (bringing A to 15 and B to 13, so A wins alone), and you never actually get to claiming the 2 power that would bring B to 15, too.