Thanks for the help, Rick and David. We're making progress! The scodetest.cgi is indeed running now and shows that GD and GD lib are installed, but scode itself still generates the "image cannot be displayed because it contains errors" message.
It looks like the required files are being created in the /tmp/captcha/ directory and that the code is being sent to my comment entry window, but the image itself isn't generating. The plug-in's author is pretty adamant that when the image doesn't show, GD and GD lib are the problem. Since scodetest and my cpanel both shows both are installed, that suggests to me a related problem the author suggested: that perhaps they need to be reinstalled in a particular order: "Once GD is installed, then install the GD perl lib, the image pop-up. (Note the sequence. You install GD first then GD perl lib..the other way round wont work.)"
Is it possible to have someone reinstall them in that order to see if that's the problem? (I'm sorry, I don't know if this is something that can be done just for my site or if I'm asking for a TCH-wide action -- if the latter, nevermind.)
Thanks,
Chuck