I'm sorry, but it is impossible to tell you what to do with the information given. You can troubleshoot it with a voltmeter, but there is really other way to tell.
But you have a much larger problem in that there is no ground. Without a ground, you must use a GFCI outlet, and they cannot be switched; both of the outlets on a GFCI must operate together and there is nowhere to put both a hot and a switched wire. It is both illegal and very unsafe to put a grounding type outlet in without a ground (unless it is a GFCI), and you can't purchase an outlet that is not a grounding type.