Sorry, I kept looking and finally found the answer to this and fixed the problem.
Check out this thread: https://www.ads-software.com/support/topic/cant-view-wordpress-properly-from-other-computers?replies=6
I had previously changed the Site Address URL to not be localhost. Changing the WordPress Address URL to also not be localhost fixed the problem. Other machines were apparently using the localhost address to access the CSS and not finding it.
Terry