Aha...another satisfied "Chasing Dreams" fan! :)
I was about 18 or 19 when I first saw this movie. It was around the time my mother and dad got their first VCR, and they decided to rent a slew of movies they had missed at the theaters in the years before. My mom thought Kevin Costner was a "hunk", and she was sold on this movie by Kevin Costner's picture on the video box cover. (This was around the time Costner made Bull Durham and Field of Dreams, and I believe Chasing Dreams had some sort of baseball theme to it, so she assumed it was a similar type of movie with Kevin in it.)
I watched it with her, and KC was indeed in it, like you said, for about 2 minutes, as the main character guy's older brother leaving for college. He wasn't seen again from that point (about 5 minutes into the movie). My mom kept saying, "Where's Kevin Costner? I don't think he's coming back...". Sure enough...he didn't.
We suspected, due to the overall quality of the movie, that it may have been made by a group of film students, of which Kevin Costner was one, before he was nationally known. When he had several box office hits, perhaps the producers of Chasing Dreams dug it out and released it on video, promoted KC's bit part, and hoped to glean a few bucks from unsuspecting fans.