I actually accomplished what I wanted with the following:

ActiveSheet.Protect UserInterfaceOnly:=True

I don't think there is an issue about locked versus unlocked, because
it works fine now. Before, I had protected two sheets  manually (not
the whole workbook) with no password and the protection worked; then
I had attempted to unprotect  them at the beginning of my routine and
then protect  them again at the end. I have no clue why what I did
before didn't work.