Hi there, sorry for the delay in releasing your post - it was caught in the spam filter for some reason. A couple of thoughts:
1) ANOVA (and other regression models) do not assume that the marginal ("overall") distribution of the dependent variable is normal (
link). ANOVA does assume that the distribution of the DV is normal
within each group. That said, testing this with a Shapiro-Wilk test is virtually pointless: If the sample is small, the normality assumption matters, but the Shapiro-Wilk test will have poor power to detect violations of normality; if the sample is large, the Shapiro-Wilk test will have good power, but the normality assumption probably won't matter (due to the central limit theorem).
2) A non-significant Levene's test statistic indicates
a lack of evidence to reject a null hypothesis that the variances are equal. It doesn't necessarily indicate that the variances are homogenous; a non-significant result might just be due to low power.
3) A Kruskal-Wallis test is a non-parametric alternative to ANOVA, but it tests a completely different null hypothesis (that the mean
ranks are equal across the populations). That might not be what you're interested in testing. If all you're worried about is normality, a simpler alternative would be to use ANOVA, but apply bootstrapping or a permutation test to calculate confidence intervals or p values.
Hope that helps!