iPad shuts down as soon as removed from charging cable.

OK, I have done some more diagnoses, which basically meant that I tried to get my head around as to why my iPad which was working fine all of a sudden has developed this behaviour. Also I tried to contact Apple support via phone but couldn't get through to them.

So iPad as I said earlier works fine if connected to the power supply but shuts down soon after the cable is removed. However I have noticed that if an app is running e.g. currently the iPad is off the cable but I have angry birds app on and running then the iPad don't shutdown, it is actually when I switch apps or go to home screen or use the power or home button that iPads shuts down...

any thoughts guys?

The battery is also draining as usual while I run these apps. do you think it is a good idea to fully drain the battery, recharge full and see what happens?