Please understand this and try to make your host understand this ...

I go to:
http://www.your_domain_name.com

I am magically redirected to:
https://www.your_domain_name.com

Right there something is controlling your domain and needs to be fixed ...



I go to:
http://www.your_domain_name.com/store

I am magically redirected to:
https://www.your_domain_name.com/store


Until you fix the first problem, the Zen Cart store CANNOT be fixed as it is being controlled by incorrect settings on your domain ...

These may be in an .htaccess file ...

Speak to your host and find out why your site is currently change to secure when you try to go to the non-secure:
http://www.your_domain_name.com