Finding important correlations

I have a question that relates to a project I've been assigned at work. I am supposed to analyze accounts that we have had in the past to determine if there are any variables that predict whether a current account will be a success or not. We have defined what success means to us, but there are many fields to analyze. It would be easy to look at one field at a time to see the correlation between those values and a successful account, but I was hoping I could do a more in depth analysis to see if perhaps the presence of more than one aspect both have a correlation. I do not know if there are any standard statistical tests designed for this, or if there are methods or software that could be suggested to point me in the right direction. Thank you for any information.
Sounds like you're looking for multiple regression analysis. The standard Excel Analysis toolpack has the regression tools necessary to do this. Essentially it gives you the correlation coefficient for any number of variables and will tell you to which degree each correlate. However to do this, all of your variables need to be numeric. So your definition of success will need to be expressed numerically.