I think the difficulty here is that the rulebook definition of “Play” specifies the cards are only played from a hero’s hand. The card played by Arcane Cadence does not come from the player’s hand, but rather from Cadence’s strange little limbo area.
Unless someone wants to argue that the played card goes into the players hand first before it enters play?
We know that "play" doesn't just mean from your hand. We have a ruling that Timeshift can be used even if hero cards cannot be played, becauase it says to "put into play" and not "play", which are two different things. If you can only play cards from your hand, this ruling is irrelevant.
Page 1 of the rulebook
Whenever a card says that you can do something that isn't provided for in the basic rules, the card is correct.
Arcane Cadence says to play the card. While the glossary states that cards are played from the player's hand, it does not state what happens when something is played from another source. Since we are in this situation, the card is right. That means we do what the card says, which is to play the card.
Except that “put into play” and “play” are distinctly different, and we know that. Timeshift bypasses the Impulsion Beam, I think that is clear. The question is what does Cadence do? The text days to “play” the card, but the rulebook definition said that cards can only be played from hand. If Cadence read “put into play” as suggested earlier in this thread, I don’t think there would be any confusion about its interaction with Impulsion Beam.
[Edit: Ronway ninja’d]
That's a stretch. It also says that if two cards contridict each other, we abide by the one that was in play first, which would be impulsion beam.
I'm of the opinion that it goes back on top of the deck. Using the concept that hero cards can only be played from the hand to justify Arcane Cadence as a valid means to play a card doesn't sit right with me. "Play vs Put into Play" seems to be the only relevant differentiation, not "play a hero card."
See, that's the thing. If "play" only means "play from your hand", then there is no reason at all for the distinction between "put into play" and "play" by hero cards. Timeshift would have worked anyways if it says "play" because it wasn't from your hand. The fact that we have the distinction, shows that play doesn't just mean from your hand.
Also, if it was meant to work like Timeshift, it would have been worded like Timeshift. It seems very strange to have two situations that work the same way, but have different wordings.
We have a ruling that cannot trumps can.
Edit: Apologies, misread the put into play.
Heedless Lash, in Infernal Relics.
Were there any hero “put into play” effects before Infernal Relics though? I’m wondering if it’s just a terminology issue and the card may have been worded differently if the deck has been released later.
I don’t have it in front of me, but doesn’t the Font of Power say to “play the top card of each hero deck?”
[Ninja’d again… You’re too fast, Ronway :P]
Atlanten Font of Power does, and Bunker won't play a card if in Recharge or Turret Mode (just tested this out in the Mega Computer).
I think that’s fairly definitive, then. The Atlantean card is clearly not being played from hand, but Recharge/Turret stops it nonetheless. The Arcane Cadence card should follow the same logic and not be played.
I still have no idea where it should wind up, though.
Rabit's reasoning is sounds great to me. Since it was revealed and it cannot be played, it'd go back ontop of the deck.
Where is that ruling? Just for reference.
Page 11 of Spiff’s doc. He has a link there.
Thanks.
But revealed cards only go back to the deck when it says to put them there. They are discarded or shuffled into the deck as much or more often than replaced.
I'd be fine with shuffling it in or replacing it, but I'm going with put it in the trash, because the only similar situation, where a card would be played but cannot be because of Limited status those cards are always put in the trash.
Would like official word, but I don't like putting it on top of the card the card specified to put on top of the deck. Doesn't violate any rules or anything, I just prefer the other option, since it doesn't affect the rest of the card's intent, and works with the only similar situation I can think of.
Only because the card that revealed them said to do so. My interpretation has always been that, if the revealing card doesn't say otherwise, the revealed card is still on top of the deck, just temporarily revealed.
But yeah, we can probably go around and around without an official word on this, as it's all opinion. 
For all intents and purposes, I believe revealed cards never leave the deck to begin with. You just get to see what they would be.
If it just said to reveal the card, I would think it went back to the top of the deck. But because Arcane Cadence says "Reveal the top 5 cards of your deck... and play one." the card leaves the deck and is attempted to be played. When it can't be played I would then put it in the trash pile.