Same thing happened to me, but I think hubby figured out how to fix it finally.
Open iTunes & connect the phone. Then hold down both the Home and the Power button for 10 seconds. Then release the home button but keep the power button pressed until iTunes finally recognizes there's a device connected to it. Felt like it took a LONG time holding down the power button, but iTunes did eventually realize there was a device connected to it. I'm now doing a restore from iTunes.