I have experienced this problem sporadically on multiple WordPress installs over different version (though all on my own server).
Under Settings-Reading-Front Page Displays...
You can choose 'A static page' but when you go to choose a post page, the only pages that show up are actual Pages, and none of the posts. I mean, only Pages show up in list of available posts, too. This is maddening, as I really want to have a post page as my static home page and don't want to use an actual WP 'Page' for my home page.
This does not seem to be a theme problem because it happens even on brand new installs using the default themes.