The home button and dock connector are pretty close together, so it's possible that something right there went bad. I agree thats its weird that two things messed up on the iPad but since they are close together, one faulty piece could effect both items.
I have the same thing happened to me.
Don't know whether it's relevant, in my case, it's JB'ed and after I installed the multi-gesture app. I can still go 'home' by using the four fingers pinch.
FYI, for charging, it charges only when it's powered off.
I'm having the same problem. Have you resolved the problem?
Well I have to say my ipad2 has started doing this just tonight. It's happened intermittently and there seems to be no pattern to it just yet but I am convinced it's a software issue as it will work fine for a long time before not wanting to work. My iPad is only 3 months old, bought at Currys in the UK, I don't want to take it to them for repair unless I am 100% sure it's a hardware problem. Not sure if I can demand a replacement TBH but as the problem is really intermittent right now it's probably going to work ok if I took it back now.
I must say that my iPad 2 has had no knocks or bumps and has had lots of care as have all my laptops etc,so this is definitely not user neglect ;).
Will post back if there any changes.