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 N-W error structure is assumed to be heteroskedastic and possibly autocorrelated up to some lag.
If you errors are assumed to follow a first-order autoregressive process, you can use Prais-Winsten or Cochrane-Orcutt regression.
If it is longer, ARMA might work.
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.