The Zen Cart zip file does contain the entire folder structure ... you just need to be sure to retain the structure (sometimes referred to "Use Folder Names" in WinZip) when unzipping.
Here's a How-To article on unzipping files, which may help you in the future:
http://www.cse.csiro.au/library/help/guides/winzip/winunzip.pdf
Note the 5th bullet on page 2.
I believe Kim's inference, which you seem to have taken offense to, is that zipping and unzipping files is generally considered to be a basic skill when working with website scripts and for transferring files back and forth between clients and designers. When someone says they've got clients waiting on them, one would expect that "having clients" also suggests a certain degree of proficiency with standard tools. The fact that you don't seem to be familiar with zip files containing folder structures suggests that your experience level may not be up to what many would consider to be expected if one were to be engaged in providing services to clients.
I'm sorry if you take offense to that statement. It's not meant for that. Hopefully you'll take a different approach and simply use this understanding to plug the hole in your skillset, and move on with what you desire to accomplish for yourself and your client.
Additionally, if your client isn't married to GoDaddy hosting for any particular reason, do them a favor and choose a more flexible/reliable host to run their ecommerce business. There are many good hosts listed on the "hosting" page, linked from the top of this page. If you'd like more info behind this suggestion, just grab a coffee and do a forum search for "godaddy" to see the kinds of problems typical of their hosting when it comes to scripted systems such as Zen Cart.