I don't know if the tablet is supposed to be that way. It won't power on when fully charged and unplugged but when I plug it in, it powers on and I can remove the charger and the battery still works.
Is this a software or a hardware problem?
My tablets do not do this. You should be able to turn this guy on whenever you want. Unless, of course, your battery is dead. Sounds like it is a hardware problem, do you still have your receipt? Can you make an exchange?
well, the power button works since you can turn it on when plugged in, and the battery works since you remove the plug and it stays on. Are you holding the power button long enough to turn it on when it's unplugged? Is it in a case where one of the volume buttons could be inadvertently pressed?