"The small girl tried to sell the sulphur matches, but no one wanted to buy them."
Translation:Den lille pige prøvede at sælge svovlstikkerne, men ingen ville købe dem.
If there is a difference between the two verbs then it's subtle. Perhaps it's a bit like the difference between "to attempt" and "to try". Perhaps "at forsøge" suggests more of an effort than "at prøve". Where "at forsøge" is attempting to achieve something by any means, "at prøve" could simply be determining if something can be done.
The distinction is more clear between the nouns "et forsøg" and "en prøve". "et forsøg" is an attempt (perhaps one of several) to achieve something specific, or an experiment see what happens when you do something specific. "en prøve" is more like a test or a test sample.
I don't know if that helped. I know that I feel more confused now.
I'm also not sure if I'm actually enlightened now. However: Tak for dit fors/og. ;-)
This sentence is writing by somebody who hasn't read "The little match girl" in English translation. Are we going to get the "The unattractive small duck" as the next story? Buy the books don't use Google translate please.
Another option: Den praktiske pige forsøgte at sælge tændstikkerne, men ingen ville købe dem.