$0 minus the cost of a headache unless you get permission from Yahoo to use their TM. Be glad you don't have the .com, since at least with another extension you might actually have a chance to develop it.
Really, you're at the mercy of Yahoo. Period. If you develop an informational site (non-commercial) discussing Yahoo Publisher you may have a chance at keeping the site, but there are no certainties. A TM is a TM, and it matters not whether it is a .com or a .web.com (ick) or a .info -- it's all about permission, fair use and content.