The Penguin origin in the comics I always liked was the one where he was warped by his over protective mother.

His father died of a chest infection after being caught out in the rain and she became this tragic insane bird loving OCD mum who would not let him leave the house in casual clothes and without an umbrella.

Having to suffer the derision of the other children he grew into the Penguin we know and love.

It sounds like a perfect Burton storyline as even without Batman so why did he go for the Tod Browning Moses of the sewers?