You are right that it is generally good habit to check for the underlying assumptions. But besides the reasoning about goodness-of-fit tests that you can explore by browsing the questions marked with the goodness-of-fit tag, in your particular case the normality assumption is not so critical, because --as ChrisP pointed out-- you would use one-way repeated measures ANOVA, favourably with heteroskedasticity assumption, which is quite robust against departures from the normality assumption.
Research on this topic is still pending, but expecially skewness is a criterion you should focus on, as low skewness will prove the distribution of the real data's ANOVA statistic to be close to the normal ANOVA statistic. Kurtosis doesn't have that much impact any more.
However, instead of testing the point hypothesis "skewness = 0" I would suggest to do compute confidence intervals for the skewness. If this interval reaches to quite extreme skewnesses, your test statistic may exceed it's $\alpha$ error rate. If not, you can be keen.
This adresses the fact (at which ChrisP pointed) that small sample sizes would spuriously suggest your data's skewness might be 0, as the point hypothesis has not been rejected. This would be quite nasty since if you already have a small sample size, then even a small skewness is disturbing.
To find the level of skewness you can tolerate, you may simulate your dataset with various skewed distributions under your $H_0$-hypothesis that the motor function is constant and see how good it meets the $\alpha$-level.