Thanks for writing back. I have looked at the admin folder, and the permissions are all set at 644 or 755, so that should be fine. I cannot edit anything in the admin panel - I went to Configuration -> Minimum values, and I modified some of the fields. When I checked, they remained at their original values.
I do think it has to be a permission thing, but there's nothing obvious. I will call the webhost, they've been great so far, but I suspect they won't have much help to offer.