Hi alberthern, yes I did resolve it but only recently. As I said, my problem was particularly odd because it would charge, but only if it was off. Even then charging took a long time. It would not charge while it was on, nor would it connect to the computer.
Of course checking the cables was one of the first things I did - even though my iPad came with two I also used a friend's and the results were the same. I reset the settings and did almost everything else I could think of.
I thought about deleting all the apps because I suspected the problem must be coming from one of them, but it's my son's iPad as well and I couldn't risk that if it didn't work, I'd have no way to connect to my iTunes to get his apps back. However one finally showed it's hand when I went to reset my clock, which had somehow shifted 15 minutes fast, and the app gave me a warning that I had tried to cheat the game. I deleted the game and wouldn''t you know, my iPad works now. To be honest I'm still pretty PO'd about it.