ignition problem

I have a 1984 300zx non-turbo problem. When I turn the key off and take it out the clock stays on as well as the door locks still operate. It is draining my battery so I have to jump it and take off the negative cable when I park so it will start the next time I have to go some where. Is this an ignition problem or mabye a bad battery. I just bought this car and before that it had been sitting for about 2 or 3 years. I have been driving it for about a week before this started happening. Can some one please help thank you.