- mærkede / følte kassen = felt/sensed [the existence of] the box
- følte PÅ kassen = felt (as in using the hands to feel/discover/learn) about the box. "Følte på" means that this was a conscious behaviour that lasted for some time. Simply 'touched' would be "rørte ved".
I'm a native Norwegian, so not an expert teacher in Danish, but I find the use of mærkede strange in this exercise; I wouldn't use this word here (and in Norwegian/Swedish you certainly can't use it like this). To me, mærkede (at mærke) referes to sensing something that's near you or detecting something/discovering it's there. I would by default use følte (at føle) to describe the process of using the hands to feel/investigate/analyse/discover the details of something.
That would be "følte PÅ" in the Scandinavian languages, Isaac_Luna_ In English, the sentence sounds even stranger to me ...
In both languages, I would interpret the følte XYZ / felt XYZ in the meaning of sensing something, e.g. that something is wrong or that there's a spirit in the room... :-)
Without the preposition,