If an effect says that you may X to Y (e.g., paying Energy to gain a Power Card, Destroying Presence to skip an Event on a board), are you allowed to get the second half for free if you can't do the first half?

If an effect says that you may X to Y (e.g., paying Energy to gain a Power Card, Destroying Presence to skip an Event on a board), are you allowed to get the second half for free if you can't do the first half?

No, the second half is gated behind paying the cost in the first half. Similarly, "you may Y by X" requires paying the cost in the second half to get the effect in the first half.
While this tends to be pretty obvious when the cost is paying Energy, it's less clear if the cost is performing some other effect, like discarding a card or removing Presence.
While you must be able to pay the cost in order to get the bonus, ongoing effects can alter the final result of the cost being paid. For example, you can successfully pay the cost of "Destroy 2 Presence" even if Flowing and Silent Forms Dart By will end up saving that Presence from destruction if you do so. On the other hand, you can't attempt to pay the cost with Presence under Absolute Stasis, since that Presence only exists for Victory/Defeat – it doesn't exist as far as the Event is concerned.