Phone will not get out of recovery mode/will not update or restore

Iphone will not get out of recovery mode. I have pressed the home and lock screen at the same time, and nothing happens. I connected it to iTunes to try to update my phone or restore it, and it will not do anything. The progress bar shows up on the screen but does not make any progress and iTunes says it cannot connect to my phone. I have tried everything and went to the AT&T store and they told me to contact Apple support. What do I do now?