You need to find a npc called 'Farm Rat', catch it, then wait for the notification you 'killed' all the rats and do the turn in. Drove me nuts trying to complete it. I got a flute and tried the mini game, i went to the Bartoli farm to get the sweet-smelling rat poison but couldn't. I finally found a listing for farm rat and it said it was associated with this quest. I found mine at the bottom of the stairs after destroying some barrels 'n stuff.