I'm a master student currently working with taxonomy and cultivation of wild edible mushrooms. In my experiment, I'm evaluating the effect of 4 distinct solid culture media and 4 temperatures on the mycelium growth and the biomass production of different mushroom strains. A separate experiment was done for each strain, with 10 replicates for each treatment. Statistical analyses of the experiments are being performed in R.

The data of the dependent factors (mycelium growth in diameter and dry biomass in grams) from one of my strains were homoscedastic and normally distributed, according to Levene and Shapiro-Wilk tests, so I ran a 2-Way ANOVA and T-test with no problems. But the data for one of my strains are barely homoscedastic according to Levene test, and not parametric according to Shapiro-Wilk, even though the scatter plot of the errors seems to follow a normal distribution with some outliers at each end. I tried removing some apparent outliers to see if it would fix things, but it doesn't seem to work. 

So... What should I do? I'm not really fluent in statistics or programming, but I know the basics.  I've spent the whole day stressed out trying to fix this, but I just wasn't able to. 

I know that you can do a Box-Cox transformation of non-parametric data, but honestly, I just don't know how to do it, I was able to obtain the lambda number, but I don't know the command for transforming the dependent factor data, tutorials I've seen online only show how to transform the independent factors. Furthermore, I also know that Kruskal-Wallis test is a non-parametric alternative for t-test, but is it the best option for my case?

Thanks a lot in advance.