After an hour or two (or three) trying to figure out why my attempt to insert Google's AdSense failed, i finally found the answer. As it often is, it was simple and stupid.
After turning off my Adblock Firefox extension, the ads showed up neatly just where I wanted them to be. That explained why the correct code appeared in the source code, but no ads were showing.
Hopefully this post may help someone else in the future.

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