Parametric or Non-parametric Analysis with z-scores?

I last took a stats course in 1999, and I could use some help in remember options available for an analysis of z-scores.

I have z-scores on 4 cognitive tasks for a group of patients and controls. I've been asked to find a way to compare the z-scores between the two groups for the 4 tasks, in a 2x2 analysis.

I've tried to refresh my memory by consulting stats books and searching google, but what I've gathered is that z-scores are mostly useful for comparing task performance within individual by standardizing the scales for the different tests. I've yet to find a way to analyze the variance between the two groups on their performance for the different tasks.

Any ideas?