In order to send you mail, Word Press uses sendmail. Without sendmail, I don't think that Word press will send out emails (don't quote me). If sendmail is disabled on Godaddy Windows, you might want to ask Godaddy if you can switch to linux if it supports sendmail and you don't have any need for windows. Does Godaddy support sendmail on linux? I imagine that you will run in to cases down the road where sendmail could be helpful. I would try to get on a plan that supports it.
To get Word Press to get your mail that you sent to your blog, you either need to view a page on your site every time you want the mail to be recieved by your blog (can't remember the URL off the top of my head-the codex might help) or get WP-Cron, the plugin for skippy.net. I used to use this plugin. It triggers the URL for you automatically, and posts post themselves. It worked great for me! Be sure to activate BOTH WP-Cron and WP-Cron-Mail on you'r blog's plugin page.