My iPhone 5 was stored in a drawer for about 2 weeks. When I took it out to charge it, everything went as normal up until the Apple icon showed up. This is when the Apple icon started to pop up and then the screen would return to black, then the Apple icon would pop up again, then the screen would return to black, and this kept on repeating. Later, I tried to plug my phone to my MacBook pro and iTunes wouldn't recognize my phone. The Apple icon showing up and then disappearing happened when it was plugged into my laptop as well.
The USB wire works with my sister's iPhone 5, so does the wall plug. My laptop also recognizes whenever my sister plugs in her iPhone so it's not the wire or laptop's fault. I've tried holding the menu button and off button for 30 seconds, a minute, and two minutes. Nothing happens. I'm not sure what the solution to this'll be. I've tried everything I can think of before taking it to someone professional.
