Our college-age nephew is a huge Star Wars fan, but he liked Star Trek 2009; so when he visited, I played him the (second) pilot of the Original Series. He was polite but yawning by the time it was over.
He had to ask me whether the episode was well thought of, whether people thought it was a good episode or not; I guess he couldn't tell for himself and wanted to know if it was representative. I told him that I thought the story and acting were good, but that it was very early in the series and some things evolved afterward.
He was just visiting at Christmas when he was here, so I don't know if I'll ever get the chance to show him another episode or if he will look on his own. From time to time on my Facebook page, I post Star Trek stills from Memory Alpha and Trek Core, in case he can see them.
I think he said he's seen Next Gen and liked it alright; but it's really hard to convert someone who only has six movies to deal with in order to be a fan -- to a thing that has 700+ episodes and 12 movies.
I feel confident the reason Star Wars has more fans than Star Trek is that it is easier to get into -- in addition to being fantasy, where Star Trek has science fiction that involves human beings and Earth.
Our nephew is a good kid; but it probably helps if a young person has a kind of academic interest in history or fondness for the mid-century modern era. I don't know how many of those there are. I don't give up on them, though; tastes change over a lifetime and usually they deepen.