Not sure what you mean by 'core' files', but if they're error log files, the contents should tell you what the site is doing wrong, if anything. How are these files named ?

You might also install this:

http://www.zen-cart.com/index.php?ma...roducts_id=860

and check the logs it creates (if any).

Your site is a little slow, but I can't see anything on it that would cause that.