Ok - try this - if you have a cpanel go to fantastico - see if they have zencart 1.3.9h in the ecommerce section.
If yes, install it that way - my host has this option and I've never had a issue with it.
It will set up (or at least my host) the database for you and put all the files into the right spots and presto - base store setup accomplished - you will then need to set up a 2nd admin so you can both start working on it.
HOWEVER BEFORE YOU DO THIS - use filezilla - download all the zen-cart files and structure - then save them somewhere - you then have a copy of the original files in case you screw up in your tweaking.
Then when you do your tweaking get the files set up so that they become your template (leaving the original files alone) - then you use your templates to run the store.
Try doing it on a local (your desk top) server so you can see them there instead of directly online.