If they show up as a shadow card do they go in discard pile, or does their effect still trigger (i.e. if would be discarded then attach to a troll)?

Based on existing rules precedents, both objectives do NOT return to play when discarded as shadow cards.

The effects on Troll Key and Purse are quite similar to that on Banks of the Anduin (although the latter's is a forced effect rather than a passive ability). Per the FAQ (p.7), Banks of the Anduin does not return to the top of the encounter deck when discarded as a shadow card. This is due to the fact that, "[w]hen a card is drawn as a Shadow card, only its Shadow text is active."

If we apply the same principle to the Troll objectives, only their (nonexistent) Shadow text will be active when they are revealed as Shadow cards. As a result, they won't return to play.

That being said, FFG has already issued one clarification pertaining to these objectives, so more may be forthcoming.