I've been having this problem since I can remember but I am now looking to back up photos and wipe it due to getting new phone.
When I plug it into the computer it makes a sound like it picks it up and the phone starts charging but it doesn't show up in devices or iTunes. I have gone through other forums for answers and have got Apple Mobile Device Support installed but nothing seems to be working. My computer has also got Windows 7 installed.
Otherwise while this may not be the easiest way to handle the problem it has worked for me with troubled Apple software. Un-install Apple Mobile Device Support reboot and re-install. If that doesn't work then un-install it again along with iTunes, bonjour and every other apple program or service. Then re-install.