Speaking from second-hand knowledge (my mother was a copyright and patent attorney):
If they truly ran said cartoon without your permission, and there's nothing hidden in any type of agreement between you and the newspaper in question (I trust your assumption, but you still might be wise to check around), then the paper is, in short, boned.
Copyright infringement is a big, big deal. A small fee? Oh my no, Clavus, you can sue them for thousands, easily. If you truly are an independent contractor (and, in which case, are no more personally affiliated with the paper than, say, I am), you can tear them a new one. If you get a really good lawyer, you might be able to own that paper by this time next yeat
(just kidding, but you can get a large amount in personal damages if you really want to take them to the cleaners).
Copyright and patent laws are some of the oldest and most strict in our nation. There's plenty of cases in courts already. Basically, the newspaper made a big, big mistake and will have to pay in some form or another.