Well, I guess sometimes writing out the problem can help focus the issue in one's mind. I Googled for other download sites of Express Scribe. Eventually I found one that was still linked to an older version. I uninstalled the new version and installed the old one. Voila, my files are working again!
I hope NCH gets this solved. I liked what I was seeing on the new version - you know, except for that whole "can't play my files" thing..
Laura