That last fact is the most important for regression i.e. the residuals were not normally distributed. If this is the case, then simple linear regression may not be best. The values for the dependent variable do not need to be normally distributed, nor do the independent variables.
It is interesting you said that the data represent the entire population. In this case, you are not estimating any parameters, i.e. the correlation coefficient. Since you have data from the entire population, you know the population correlation coefficient, no confidence interval, no test, it just is what it is. Speaking in these terms, I feel that by doing a regression, you are just finding a line that best fits the data. Typically people will then find a confidence interval for coefficients. In your case this is not necessary, because the coefficient you come up with is the population coefficient. I would go with the regression if it tells the story you want to tell about the data. But keep the above discussion in mind when you need to explain.
Disclaimer: Others may disagree with my assessment, including statistics instructors. Perhaps one of the moderators of this forum will comment.