Well, you should probably delete that /store/ subdirectory that's showing the need for a new install if that's not really the actual folder for your store.
And then you'll have to sort out with your hosting company what exactly is causing the 403-forbidden error. The server's error logs should be explaining the cause, and if you can't access those then your hosting company will have to do that for you.
It's essentially impossible for us to guess what exactly your "store.xxxxxx.com" subdomain is pointed to and what exactly is causing your server to throw an error that Zen Cart has no control over. That's a server error, not a Zen Cart error.
It's also interesting to note that your subdomains are what's broken, and not the running of the store from its folder, as evidenced by your store_new "working". Again, points to a server configuration problem, perhaps in how subdomains are configured.
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