I had a similar problem with my IPAD 4. Strangely it connected to ITunes on my desk top but not my lap top. The problem was a missing device driver.
With my IPad connected to my lap top,I went to Control Panel, Devices and Printers, there I could see that an IPad was connected but had no driver associated with it. From that display I simply asked it to find the new device driver. Which it did and now all is fine.