Here is a spreadsheet I created to test the effect of various stock prices and market caps on price and value weighted indices. You should create a similar spreadsheet (though formatted better -- the first sheet should be a summary with a description of what you are doing and the important results, i.e. the correlations). You can also add in interesting charts and possibly an equally-weighted index.
Note, by pressing 'F9' you'll recalculate the '=RAND()' functions, which will give you entirely new correlations. You could hit 'F9' many times, recording the resulting correlations, and get a Monte Carlo estimate of the correlation distributions. A macro may be effective in doing this.