Like Demo this sounds vaguely familiar to me, but I can't remember what the problem was.
Do you have a second computer and/or know anybody else with iTunes on their PC that you could try the iPad with ? If it's recognised correctly on that then that would kind of imply that the issue might be related to this PC as opposed to the iPad.
I've now found this post about the iPhone which seems to be a similar issue :
You could try what the last post describes - though unfortunately the original poster didn't reply as to whether it fixed it, but it could be worth trying.
There is also this thread which, though it refers to the old Find My iPhone setup causing a problem, you could still try what it suggests i.e. renaming your iTunes library and trying connecting the iPad with a 'clean' library :