If you face issues in receiving /sending mails via Outlook/Outlook-Express/Thunderbird, you can try using direct IP in place of incoming and outgoing server.

Also, you can try using port 465 (with SSL) or port 587 (with TLS) as outgoing port. For POP port 995 (with SSL) can be used, and for IMAP port 993 ( with SSL) can be used. (Note: Certificate warning should be accepted by clicking YES)

Do provide us with the results of the following three commands (on Windows platform) mentioned below if you continue to face the issue:
Go to Start Menu>>Run>>cmd>>
>ping <your-domain-name>
>tracert <your-domain-name>
>telnet <your-domain-name> 25

Send us the print screen/screenshot of above commands

Make sure port 25 is open/allowed in your antivirus, firewall, and also at ISP end.

Also, make sure 'My Outgoing Server Requires Authentication' is ticked YES

Incoming and Outgoing Server should be : mail.<your-domain-name> Email username should be full email address : (username@<your-domain-name>) Password should be tested at webmail.<your-domain-name> and also re-filled in the password field in Outlook/Outlook-Express/Thunderbird. If it still does not work for Outgoing, it is best to reset it from within cPanel

For google apps users, following knowledgebase link should be useful:
http://support.google.com/mail/bin/static.py?hl=en&page=ts.cs&ts=1668960&from=75726&rd=1

Thanks

Ashutosh