That sounds like the problem is with the cert and your preference for non-www'd URLs. The cert is provided for either www or non-www but not both so ask GoDaddy to use your preference (as configured in your ZenCart config files).
I don't know how GoDaddy installs https but, if it's in a different directory (not shared with the non-secure website), that might be another source of problems. These days, very few hosts do that, though.
While you're at it, I'd also recommend using a good host rather than a registrar for your hosting. GoDaddy has a terrible reputation as a host while their reputation as a registrar is pretty good. Of course, if they fix the current problem, then the hosting choice is up to you.