I enjoy kayaking, hiking, tennis, volleyball, skiing; and I really want to learn how to snowboard this winter.
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It looks like what you really want is an em dash (—) to go with the asyndeton in your first clause:
The dash turns the balance of the sentence into an anacoluthon (i.e., a change in direction or a break in structure), which is another rhetorical device used to express urgency or excitement. That's what you seem to be going for by piling up words one on the other, and finishing with the climactic announcement about learning to snowboard. The change in direction is from things you currently enjoy to something you intend to do.
Now, strictly speaking, you could view your sentence as a simple enumeration, and that is how others seem to have understood and answered the question. I find nothing wrong with their answers. Still, you may not be asking the right question for what it appears to me that you actually want to express.
There are a couple problems with that sentence. First, a list usually ends with "and (last item)"; you're missing the "and". (There is an argument about whether "and" should be preceeded by a comma; I'm not addressing that here.)
Second, if you want to use the semicolon to separate two clauses, then the clauses must each stand alone. Technically "and I really..." does, but it would be stronger without the "and". With the "and", you could just as easily use a comma instead of the semicolon.
So, to sum up, the following would be correct and better than what you have:
Larry Trask advises
That makes the semi-colon in your example unnecessary.