Can I assume Normal Distribution?

I am comparing 5(groups) experimental data sets with one Control Group. I am trying to determine which Experimental group is better than the Control group.

I am measuring blood volume, so the better group is the one that had higher blood collection.

Each group has 80 data points. Each data point is independant. Data sets are suppose to be representative of the population. I can determine why they wouldn't be.

Goodness of Fit tests show that:
Control Group is rejected as normal
group 1 is rejected as normal
group 2 is rejected as normal
group 3 is NOT rejected as normal
Group 4 is NOT rejected as normal
group 5 is NOT rejected as normal

Based on my understanding of comparing normal with non-normal data, I can only use the KW Test.

Is there any reasoning to justify the data being normal so that I can use ANOVA/t Tests/f Tests since the data sets are large?

Thanks for any guidance.

I would first apply Levene-test for checking if there are deviation of homogeneity of variances. Several test stats are robust against not to strong deviations from normal distribution of the data. If data are non-normal distributed or varianvces are not homogenious etc. why not transforming data? (e.g. square-root +0.5) There are many possibility depending on the form of the of data distribution.
Another possiblity is the use of multiple t-tests with bonferroni-holm adjustment of alpha error if I remember right.