As you say, the question pronoun corresponding to
Ich komme nicht auf das Netzwerklaufwerk
is wohin, so it's rather a determination of the direction than of location. This makes the difference because the prepositions
an, auf, hinter, in, neben, über, unter, vor, zwischen
are called Wechselpräposition and can govern either the dative or the accusative, changing their meaning. When they describe a location (as in auf dem Netzlaufwerk speichern – wo?), they govern the dative. If they are used to indicate a location (auf das Netzlaufwerk kommen – wohin?), they go with the accusative.
As a native speaker, you will intuitively understand the difference between Ich gehe auf dem Boot (dative) and Ich gehe auf das Boot (accusative).* You might also have heard the verb kommen getting an insinuating meaning when used with a Wechselpräposition governing the dative (see no. 17 here): Ich komme auf das Sofa (accusative, direction, standard meaning) vs. Ich komme auf dem Sofa (dative, location, insinuating meaning).
*This example is similar to tofro's, but better comparable to the original sentences because it's neuter as well and hence uses the same articles.
