In Recent YAHOO MAIL theme modification ( After October 2009 ) you will not find direct link to compose page with “Write New email” or “Compose” as anchor text. To compose new email you should just click on NEW Button (Right side of Check MAIL Button).
If you click arrow last portion of “NEW” button, you will see option of sending SMS and CHAT message. Sensing SMS from Yahoo chat is not free service. There are many other website from which you can send SMS for free to any mobile number.
Other long method to find compose page is, just reply any email, delete the subject line, email address, and text, your compose page is ready for new email.