I would take the board out and clean it with a toothbrush and rubbing alcohol as this seems like a problem relating to the motherboard. Also, your hard drive and data are likely fine, the motherboard just probably doesn't recognize hard drives anymore. Cleaning the corrosion off of the board is a good start to get your Mac in working order again!
What came off is a layer of the LCD. It broke off from the other layers and stuck to the broken glass. To repair the phone, you will have to replace the entire LCD since the old one is now broken. Glass only repairs are usually very difficult and risky on most phones, so don't fell bad!