Phone is off / black when I plug it into charger, only the Apple logo is displayed
Give TinyUmbrella a try. It's a powerful tool to exit the recovery state of the iPhone without the data loss.


Make sure that your iPhone is on (showing the Apple logo in your case)
Connect your iPhone to your computer via USB
Download and install TinyUmbrella
Launch TinyUmbrella and wait until it recognises your iPhone
As iPhone gets recognised press exit recovery shown in the main menu