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Have you tried different USB cable ? Have you tried restarting your Mac ? If not, please do this.
If it still not working, then we can soft-reset your iPhone and see if it works or not. Disconnect it from your Mac. Then press and hold down the Power button and Home button at the same time until it shows the Apple logo. When you see the Apple logo, release the buttons and let it boot. Connect it to your Mac and see if it works or not.
Please let me know if that didn't work, so we can continue troubleshooting.
When you connect it to your Mac, does the iPhone make any sound ?
Does Image Capture application recognize the iPhone ?
To make sure this is not an issue with the Mac, first reset the System Management Controller of your Mac. Follow the steps below;
Shut down the computer.
Plug in the MagSafe power adapter to a power source, connecting it to the Mac if not already connected.
On the built-in keyboard, press the (left side) Shift-Control-Option keys and the power button at the same time.
Release all the keys and the power button at the same time.
Press the power button to turn on the computer.
If that didn't work, then reset the PRAM and NVRAM of your Mac. Follow the steps below;
Shut down your Mac
Restart and immediately hold down Command-Option-P-R keys at the same time
Hold the keys down until the computer restarts and you hear the startup sound for two or three times.
Release the keys and let the Mac bootup.
Check iPhone. Does it work now ?
Sure. We can continue any time you want. Add a bookmark of this page or add this page to your favorites, so you can get back to me later.
When you get back, please do the SMC and PRAM reset and let me know the results.
Do you have another Apple device there to test on your Macbook Air ? Or another computer to test the iPhone ?