Try these:
First open iTunes and connect your USB cord to your computer, but do not plug it into your iPhone. Then press and hold the home button on your phone while connecting the USB cord into your iPhone, while continuing to hold down the home button. Then click restore in iTunes.
If the battery was dead for a long time, you may have to leave it on the charger connected to an outlet (not USB from computer) for awhile. Sometimes works.
Try a reboot with the phone plugged into an outlet.