For a Zen Cart that old, I would certainly upgrade it where it is. The reason being that if it's working there, you are very lucky. If you tried to transfer it to a server using up-to-date versions of PHP and MySQL, it would probably fall over.
Upgrade in this sense means upgrading the database using the database upgrade facility in zc_install (ensuring that it is properly backed up first). There's no point trying to upgrade the template of a site this old. You would need to re-build that.
Indeed, with Zen Cart 2.0 just around the corner, also requiring a template re-build, is this a project that could be dealyed for a couple of months?
Kuroi Web Design and Development | Twitter
(Questions answered in the forum only - so that any forum member can benefit - not by personal message)