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What exact message are you getting when you connect ?
Sorry for the delay. Can you connect using different USB cable and see if it is working or not ?
To understand the problem, have you tried connecting this phone to another computer and see if it works on it ?
Also, soft reset your iPhone and see if it works 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. This will soft reset it. Then connect it to different USB port of your Mac and does it recognize it ?