This is the strangest fault I have ever heard....
As a pure guess, something being loose on the inside of the screen/hardware interconnection might make sense, and when the USB is connected it pushes this connection together.
No amount of software work around would touch your fault from what you are describing, because a software fault would act differently. If being connected to a power source or a input such as your computer made the difference, then you could wonder out loud if a software fault was the culprit. The way you are describing it, I can not see it being software, so of course the hard reset would not help.
Sorry, but I think you need a Samsung agent to help. This has to be 100% on the build of the phone, not on the OS. Again, I am not a tech guru, but truly this sounds like something AT&T or MS would not be able to help you with. See if you can get on a Samsung Mobility website and get a chat going with a technician.
Let us know what you find out!! Sorry I can't be more help.