If you trash Earthrise Hotel with Aesop's Pawnshop, do you still draw the 2 cards? I'm aware of two related rulings that lead me to suspect that you do.
1. Aesop's + Wyldside: If you trash Wyldside, you still get 2 cards and still lose a click on that turn. My understand is that this is because the "When your turn begins" effects are all resolved even if the card generating the effect leaves play. Essentially, Wyldside's effect takes on an existence that is independent of the card.
2. Aesop's + Daily Casts: This is different because Casts' effect is to "Take 2c from Daily Casts." Like with Wyldside, that effect resolves even if Casts is trashed, but since the card will be in the heap at that point and the credits will be gone, the effect doesn't actually do anything.
Applying the same logic to Earthrise Hotel:
Earthrise's effect is "draw 2 cards and remove 1 power counter." Earthrise will be in the heap by the time that effect resolves, so obviously the "remove 1 power counter" part can't happen. But does that prevent the "draw 2 cards" part of the effect from resolving? If it does, then the runner will get the $3 and the 2 cards as well.