Windows 7 Home Premium 64bit: VPN connects and allows access to network's Unix Server, data entry, etc. However, Outlook 2007 receives but does not send messages, error 8x800ccc78. When the VPN is not connected, messages can be sent (and received).
I would verify if all Ports are opened up for VPN and Email (SMTP Port). Depending on your Email Provider, look in your Outlook setting if the Outgoing Server might requires authentication. If VPN is blocking your SMTP, you may use an SMTP Relay, 100% sure that your email will send out.