Where it processes through to the thank you page, the email has been sent to the SMTP server, but the SMTP server is not relaying the message to the recipient.
First, for the From settings, set only the from email address, some server will fail to relay the message if a from name is set to.
Another thing to try is on the mail server settings tab, click the "Include From Address Using Additional parameters" Option.
If the email is still not coming through, you will need to contact the host and have them look into the SMTP servers error logs to see why the email is not being relayed.