Part of the problem isn't the DBI, it's that the SQL query you're trying to construct really isn't valid -- or at least won't give you the results you expected. In your final example:
SELECT name FROM catagories WHERE catagories.workrelated = ('Y' || 'N') ORDER BY name

MySQL is going to perform a logical-OR on 'Y' and 'N' and come up with a 0. So your query is logically equivalent to this:
SELECT name FROM catagories WHERE catagories.workrelated = 0 ORDER BY name

Remember that logical OR is going to take two arguments that are either true or false (or nonzero-but-numeric and zero in MySQL's case) and return a true or false (1 or 0) result. You could rewrite the query like this:
SELECT name FROM catagories WHERE catagories.workrelated = 'Y' || catagories.workrelated='N' ORDER BY name

Or better yet do as bart describes and use IN('Y','N') instead.

By the way, for the sake of programmers who may follow you, I would suggest spelling your table name categories.

        $perlmonks{seattlejohn} = 'John Clyman';

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