I don't have it on my computer - I loaded it here.
It would make sense that you loaded Zen cart onto your site server, and not your PC. It has to be on a web server host (such as LP) to be useful to anyone. Of course, you can set up a PC to be a web server host, but that's harder than buying services such as LP's...
Can anyone help. Should I download it to my computer - if I will - will I be able to find the admin area - which I can't seem to find here at lunar.
No, don't download it to your computer.
If you properly installed Zen cart, the admin area should be on your server. If you installed Zen cart to
http://www.mysite.com/store/, for example, the admin area is typically something like
http://www.mysite.com/store/admin/. Maybe it's under a slightly different name -- the installation instructions should tell you (e.g., .../zen-admin/). If you messed up the installation, there's no telling what's there.