May I use the Newey-West procedure when I have only autocorrelation?
Or can I only use the Newey-West when I have autocorrelation and heteroscedasticity?
The short answers are YES and YES.
The Newey-West estimator is one of the so called heteroscedasticity and autocorrelation consistent (HAC) estimators of the covariance matrix, it's not the only one out there. It works for any combination of heteroscedasticity and autocorrelation present.