How to choose a statistical test to compare brand ranking survey results?

I have 100 people who have answered a brand ranking survey about 10 brands according to 9 descriptors (new, good features, perception etc.) I have to rank the 10 brands using a suitable analysis: I basically started by finding correlations between the descriptors and then removed ones which were not useful, and then found the mean and ranked by mean. Is there a better way of doing it? I also have to use a suitable statistical test to examine the relationship between the brand ranking and the descriptors. How would I go about this? I heard that the Kruskal Wallis Test is the best one because the results are multivariate, would anyone agree, disagree? It's non-parametric data so just not sure which test to use... thanks!