Probably your network provider is restricting outgoing mail, as it is frequently a sign of a spammer or a compromised machine. If you find the instructions from your provider for configuring an email client for their network, you should be able to configure sendmail (or other MTA) the same way. This will probably involve using your username and password to authenticate with their SMTP server as the next hop to connect to. This may be called "smarthost" in your MTA config.
If you have a specific error that you are seeing though, it could be completely unrelated.