Seems like a battery issue. The battery performance has decreased, due to its age, so much it cant even boot the phone. A good battery for a iPhone 4 is roughly $15-$30 As for the screen getting darker. That can be a multitude of things. The most common thing i have found to cause that is either the battery or a bad screen.
Personally I would get the new version controller from a Microsoft store, not online. Or bring it into a store and see what they can do about it. It might be just a coincidence that both controllers are bad.
A back glass repair is virtually impossible without breaking any internal parts. Apple doesn’t sell their OEM parts like Samsung does. I would bite the bullet and get a case that covers the cracks or spend Apples premium to get it fixed.