Screen burn and not turning on, is it fixable?

@worsergeor24709 the screen looks like it is delaminating and damaged. You most likely will have to replace that. Since your screws "were black and rotting" it is best if you consider removing the board and cleaning it with some isopropyl alcohol and check for any damaged components. You could be running into a corrosion issue.

To remove those stubborn screws, I usually use a Dremel or similar tool. Then I drill trough the screw just enough to drill teh head off (drill size is the diameter of the screw thread). After that remove the rest of the screw from the case with a pair of pliers. There are also screw extractors that may work for your screws
Use these guides to work on it Game Boy Here are the screw extractors Precision Screw Extractor Set Use this guide. to clean the board. Yes, it was written for an iPhone but all the steps are pertinent to your board as well.