You can use "aligned rank test" .

Don't use a statistical test to determine the normality of variables. The problem is that they are sensitive to sample size: as the number of observations increases they are more and more likely to find a significant deviation from normality, even if this difference is very minor. (See: http://blog.fellstat.com/?p=61). You will be better served if you use a q-q plot or histogram, and let your eyes decide.

I don't know much about PCA, but it appears that nonlinearity and outliers are probably the biggest problems. I would recommend plotting all the variables 2-by-2 in scatter plots*. Pay attention to nonlinearity, outliers, and log-normally distributed data.

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* The PerformanceAnalytics package has a great function for this. See: http://rcompanion.org/handbook/I_10.html .

I fully agree with Salvatore: inspect histograms and Q-Q-plots. There are non-parametric alternative for ANOVAs with factorial designs; e.g., as suggested by Omar, the aligned ranks test. The ART and the ARTool package are relevant here. These are for between x between designs. For other designs (between x within, or within x within) see the nparLD package.