When negotiation fails for any reason, the Problem is not solved. It remains on the board in the same spot, and all committed resources return to their owners.
Personality cards played during the negotiation have still been played, so they are discarded as normal. Cautious players may want to mention they have a card without playing it, though this reveals part of their hand to the other players at the table. Suspicious opponents may demand to see the card as well.
If you chose the Problem as the Active player, your turn is now over. You may not choose another Problem to solve