For time out issue :
For Webmail timeout, check time limit in php.ini file.
Also check Attachement site in php.ini and webmail config, if you are having larger attachement.
For Receiving mail issue,
First of all check DNS report(http://www.dnsreport.com
) for your domain.
Are you getting proper MX records?
If not, check godaddy.com and add necessary MX records.
Check whether your firewall/router ( if using ) doesnt block smtp port.
If you are using cox.net network, SMTP settings are different, instead of mail.domainame.com, you have to use smtp.east.cox.net (Check cox.net for exact setttings).
Consult ISP if they are filtering mails at their end before sending to World.
There are lot more things to find out exact problem. But start with checking MX records.