After paying, setting up an account, validating it (via e-mail), and downloading Minecraft.exe, I double-clicked on it. It looks like some instalation process is running and, in the end, a window named Minecraft Launcher 1.4.4 displays news, information, my profile name (down-left), and a "Play" button (down-center of the window).
Clicking on "Play" will result to the appearance of a downloading bar under the same window saying it downloads "common lang", "1.7.9 jar", etc. When finished, a new window with Mojang logo appears shortly. It lasts only for a couple of seconds, it disappears afterwards, and it is replaced by the old Minecraft Launcher 1.4.4 window. Clicking again on "Play" button will conduct to the same routine described above.
That is all. Can not play.