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On the iPhone can you press and hold down the power and the menu buttons for a full 15 seconds, during that time the phone should power up then shut down then power up then shut down again.
After it has shut down the second time can you then press the power button for 2 seconds to see if it will power up cleanly.
If not can you do the same thing again except do not power it up, Instead can you open iTunes on your Mac and then connect your phone to the machine and see if it prompts you to recover the phone.
Let me know what happens