linux sendmail

I have a computer at home running linux and I want to have it email me a log file every day. I have tried setting up sendmail but it keeps telling my that the mail relay was denied.

Is this because cox blocks out going smtp ? If that's the case I will stop trying to figure it out and just have it use cox's smtp server.

Has any one else gotten sendmail to work as an outgoing email server. I don't need it to receive email.