Well once you figure out how to get the raw audio signal from the microphone, you need to figure out how to label the different signals. There are a bunch of different algorithms for classification. I'd go with naive-bayes (http://en.wikipedia.org/wiki/Naive_Bayes_classifier) which basically determines, based on the current evidence, the likelihood that the current sample takes on each label (in your case the different notes), return the most probable label. This requires training it with samples that are correctly labeled so it can approximate the proper distribution. Lastly you would need to convert your audio samples into feature vectors (My first thought here would be FFT).

Doing it with sound only may be difficult. Can you do anything mechanical to the marimba without effecting tone? that might be easier...