Troubleshooting DNS:
kloth.net
Troubleshooting the misbehaving website:
rexswain.com http viewer
Troubleshoot MX records:
mxtoolbox.com
Track down the random ISP .txt records or the exchange server that will not work remotely….
Microsoft Remote Connectivity Analyzer
https://testconnectivity.microsoft.com
IF all else fails … did you check the hosts file??