I need to decide whether or not to use a parametric paired t-test or some type of non-parametric signed-rank or rank test (hypothesis test).

Typically, when I work with smaller sample sizes, I would check such things as Shapiro-Wilk, outliers, skewness and kurtosis. Assuming that none of these raised any red flags (such as Shapiro-Wilk p-value<.05, extreme outliers....) I would assume normality and proceed with a parametric test.

However, when working with large sample sizes (such as those larger than 100), I have often been told that it is sufficient to simply look at the distribution of the sample and if it is roughly normal then it is fine to assume normality and use a parametric test.

This particular data set I'm working with now, however, is throwing me for a loop. The sample size is sufficiently large (about 120) however, it does not appear normal whatsoever - (the histogram is nowhere near close to being considered normal, the QQ-plot is not linear, the skewness/kurtosis values are very high).

Thus, I'm not sure whether I am justified in using a parametric test (in this case, a paired t-test)?

I'm also not sure what you mean by boostrapping?

Perhaps another way to rephrase my question: Even with large sample sizes (greater than 100) how important is it that things such as skewness/kurtosis, outliers...are not out of whack?