The Durbin-Watson statistic is primarily used to detect autocorrelation for a time-series analysis, not ANOVA.
You may want to look into the Kruskal-Wallis H test ranked sum test: http://www.anselm.edu/homepage/jpitocch/biostats/nonparamstats.html
There are a lot of resources on Google if you search "R Kruskal-Wallis H test"
Good luck!