Well my complete understanding of matrix is that it never actually says the matrix has been around for a hundred years. It could have been around longer than that but in actual reality, no body really knows except the writers.
About Morpheous, I would think that he is able to live that long. He is a machine, and who know's how long they actually run for. I know that they can be killed in the matrix, but that would be just like puting a virus in a computer, it's going to crash it. So I believe that he was 100 years old at the time.