You can’t receive email from external address if you don’t add receive connector to Exchange Server 2010. I will show you how you can easily add receive connector with Powershell:

Get-ReceiveConnector "Default *" | Set-ReceiveConnector 
-PermissionGroups:AnonymousUsers,ExchangeUsers,ExchangeServers

You may change “PermissionGroups”. Please use Get-help for extra information.