The "Cheers" phenomenon that you described happened with my youngest also--except not with the "Cheers" theme. My husband made up a nonsense song for her, and eveytime we sang it, no matter whether she was playing or crying, or eating or whatever she would stop and listen. This was VERY helpful when she was cranky. The song went like this, (wish I could post the tune, but it's done with a sort of Bo Diddley feel...) You might pick up on clues that tell you that Dad teaches Math and Physics...

Oh, Bonney, oh, Bonney do you have a purse? Do you have 25 pacifiers in it? One for Monday, one for Tuesday,8 for Wednesday, 12 for Thursday, one for friday, one for Saturday, and one very beautiful one for Sunday

Oh, Bonney, oh, Bonney I see you are a girl Do you know how lucky you are? Cause soon you'll be walkin', and then you'll be talkin' and then you'll learn to multiply and then you'll hate infinity, and you can be whatever you want to be.

Oh, Bonney, oh Bonney you're in our family Do you know how lucky we are? You have a Dylan named Dylan and a Britta named Britta, a doggie named Misty and a kitty named Meggie, a daddy named Daddy and one very beautiful mom named Mommy

Oh Bonney.