The website I am working on doesn't sends the orders notification email either to admin nor to the customers. But the admin and customers receive registration and reset password notification emails. I don't know why this is happening. I am facing this issue for the past 20 days.
First go to System > Configuration > Sales Emails and make sure that Enabled is set to Yes.
After that look in core_email_queue table. If there are entries in the table and customers/admin are not getting any emails it means cron job is not running.
More details here.
In magento 1.9 all the emails are queued up and then waiting for cron job to implement...
Simple cron job for cpanel user is
php -q /home/YOUR_USER_NAME/public_html/cron.php
or use this
php -f /home/username/public_html/cron.php
As per my research try one of them.
Settings of time can be as per shared hosting or VPN or dedicated. Most shared hostings allows 5 minutes you can try with 20 minutes.
Magento new order email allows notifications to be sent to administrator(s) when there are new orders placed