I think the .doc file or the Trados project is corrupt. Nothing to do with CafeTran, although CT will almost certainly be blamed.
A "Trados trainer" (what a job...) solved the problem. That is, he didn't solve the problem. There was something wrong with the source document. Not with Trados. And of course, using CT didn't help. Trados was not to blame. I think the client believes me by now.
The subject line says it all.