Well, you need to probably change your configuration in sendmail so it will listen on more interfaces than just 127.0.0.1. If you go through the sendmail.mc file it will probably tell you what you need to comment.
Also, does your client computer resolve 'hostname'? You you have a dns record somewhere for 'hostname'?
I did a quick google search and found a document you might like if you have no sendmail experience. http://www.feep.net/sendmail/tutorial/
It should help get you started anyways.
Since you are using sendmail, you can go to sendmail.org if you need help with the config file. It is very well documented.