If I try to access my site at http://mydomain.com it comes back with "Oops! Google Chrome could not find mydomain.com". I would expect it to automatically redirect to http://www.mydomain.com. What could be causing this from happening? Could there be a setting on the server? (Ive asked my hosting supplier but received no response). There's no htaccess file or anything in my code that could be preventing this.
In Webmaster Tools Im trying to get the setting so that Google recognises the website as sitting on www.mydomain.com - but I cant verify http://mydomain.com because of the issue above.
No, your browser is not going to attempt to try the www version of the domain name. It sounds like you are missing a DNS entry for the domain name without the www. You should have an A Record pointing to the IP address of your server for both www and without www versions of your domain name. The www is actually a subdomain.
Some DNS (such as that provided by Namecheap) can be set to automatically redirect to another domain. So if someone entered your domain without the www, the DNS would issue a 301 Permanent Redirect and the browser would then fetch the www. Otherwise, you can have the server issue a 301 redirect to the www version in your server's configuration file or directory configuration file such as htaccess (if you are on shared hosting) if you are using Apache.
Do a DNS lookup and see if there is an A Record returned for your domain name without the www. I have seen a few times where there was no DNS record for the without www version and this may be the case in your situtation.
Great - thanks cheesedude.