Disable your anti virus when you do the download. Thunderbird is shipped as a self extracting zip file and lots of anti virus products make a royal mess of those, or offer inane warnings about the "risks"

Thanks! I ended up downloading it on another computer and transferring it over. Oddly enough, the other computer had less anti-whatever on it than this one does. For some reason, the downloaded file size was a couple of thousand bytes larger on the "corrupt" version - perhaps it was corrupted somehow in the download process.