Although I had over 3000 documents with the word Normal in them, I only had one Normal template for Word 2008 and one for Word 2004. I had renamed the Word 2008 one yesterday and it didn't work, but as you suggested, I did that again today and it worked!!! My previous document that wasn't working still doesn't, but I opened other old ones, changed the fonts to the problem ones and sizes, and it still worked!!!
Then I began wondering about the fact that I usually am in compatibility mode, since I'm usually needing documents that are .doc, and found that if I opened one, they were fine. If I created a new one, that was fine. But if I went to preferences and clicked on the compatibility one that shows options for 2004, compatibility checker flags that I've got my preferences set for Word 6/Word 95 in any document, even if I save it as Word 2004. I tried that several times and it keeps doing that. When I went back to showing the options under Word 2008, compatibility checker was happy with all documents. I wonder if that has anything to do with my previous problem?
BUT the good news is at least at the moment I think everything may be OK!!!
Thanks to both of you, Bob and Daiya, for your unbelievable level of help with this!!!!! You are both quite terrific!!! I'll let you know if I'm wrong and this wasn't fixed after all, but it looks as if it's all set.