Pusheen

There should be gaskets available online. Get the screen, gasket for the screen and the back of the phone (so you can replace the back glass).

iOS bug. Restart the phone.

Replace the LCD panel. The black is the cracked LCD. But if your screen is laminated (if there is an obvious gap between the display and the glass) you need to get the LCD with the glass on it.

The cable if probably dead or the connector is if there is no picture. The GPU might also be dead. If that is the case, get it to a shop with board repair or replace the screen cable/connector.

Your battery is almost dead. Replace the battery because it drains too fast for iOS to notice, and if you try to do something like open an app the battery puts out more power than it can handle and shuts off.

Did you damage the home button Cable? Sometimes, the contacts on the board are touched by your hand and the oils block contact. Or maybe the home button got dust under the button?

Caulking material may work just fine, most putty sealants are much more expensive.

The video chip may have a bad solder connection. Take a fine magnifying glass to it, and check for blackened or corroded contacts. If there are any, clean it off, use flux and a nice hot soldering iron, and apply a little solder to it. The LCD connector may also be faulty. Check on that too.

First, is it charged? Second, have you spilled liquid on it lately? Third, has it been acting weird before the problem? Was this random? If one, then charge it. two, there may be no hope. Three, blown capacitor or bad charger. Four, LCD cable may have disconnected, or the LCD connector may be defective. Open up the laptop, and look inside. Check for any corroded, burned, or plain disconnected things. Clean it, check the solder joints, and try again. If not, it may be dead.

Check the screen digitizer seal. Remove the LCD and look at the little black rubber seal around the clear portion of the screen. There may also be a connection issue with the logic board where some pins may not connect fully.