LCD display is busted

Sony LCD new for this model costs US$93.60 and it is in stock.
May be you can replace this your self with a small + type screwdriver and tweezers and little bit of patience.
Do contact me

Sonyspares

Repair is not going to happen because cameras are machine made like a Timex watch.
You could contact the Sony but their answer will be horrific.
So Camera stores do sell LCD protectors. they are designed to protect LCD's before the trunk gets slammed onto them.
They are like extra thick clear tape which you can cut to size.
So if it is still working this can be a way out- Then your 3 year old can have a nearly good camera to play with.

Buy a broken DSC-P92, or even a DSC-P72 on eBay for $20 or $30. The LCD is an easy swap, and if you're mechanically inclined can swap out the screen. Your camera is only worth ~ $50 so it doesn't make sense to spend big dollars to fix it.