What is the benefit of using Newey-West when there is no impact on the coefficient estimates in OLS? Since my residuals failed the test for heteroscedasticity and autocorrelation, what is the benefit of using Newey-West when there is no impact on the coefficient estimates in OLS?
Does the Newey-West make any impact on the OLS model?
Should I use GLS instead of OLS due to heteroscedasticity and autocorrelation?

If you only want a predictive model where you take the coefficient estimates and apply that regression equation to new data, the Newey-West does nothing for you.
However, Newey-West is a pretty good way of handling unequal variance and autocorrelation in the error terms when it comes to estimating standard errors for the regression coefficients.
If you are interested in testing or writing confidence intervals around regression coefficients, Newey-West could be a valuable tool. Newey-West was first published in an econometrics journal, and much of economics deals with this sort of inference rather than pure predictive modeling.
