... but, when i try to battle, i can't, as they are hungry. What can I do?
it takes an hour for the resort to kick in
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Looks like all your pets' HP is full and they're all happy (ie. have minions) so I would double check the resort and make sure that they are actually in there. If none of your pets show up on the drop-down list for either resort then i'd suggest that you file a ticket.
EDIT: