have you tried hard reboot? press and hold home button + power for 15 seconds until you see the apple logo. release the home and power button if you see the apple logo, and wait till its boot. hope it helps.
check if your connected on the internet, and place the usb cable at the back of your pc or if you are using laptop or mac, change the usb port. and check if its detected on itunes. if its still the same problem change the cable or restart your your pc. hope it helps.
that its not the right way to go to DFU mode, if you want to put your device in DFU mode just follow this steps. plug your iphone on the pc or mac then press and hold the power and home button for ten seconds, then release the power button while holding the home button and wait the confirmation for the itunes your phone is in recovery mode. and you will recognize your screen goes black. no itunes logo nor cable logo. if you can see the itunes and cable logo, your on a recovery mode. its not DFU mode.