Aarrgh, email again!
I can't believe it. I had totally uninstalled Eudora Pro, then reinstalled it last Thursday. Tonight it did the same thing ("this program has performed an illegal operation...etc.". So I uninstalled Eudora Pro again (this is my bought copy of version 4.1), downloaded the "adware" version of Eudora Pro 5.0, and installed that. We shall see how it goes. I truly think something I installed within the last few months is causing various problems with my computer, including what has been happening with Eudora Pro, since I had never had any major problems with it before.