I assume you are using Joomla! 1.5 (an old version of JCE had a file upload vulnerability). The easiest approach would be to isolate the selected file, have the host set the site online (they probably set unreadable permissions to your public_html directory) and then perform the update through Joomla! (this ensures a correct update).
Or, we could just uninstall it and install the updated version - that is, if you don't care about current settings in JCE.
PS: I'm currently employed at a company that develops extensions for Joomla!, including a security extension listed in the JED :)