It sounds to me like either the mouse sensitivity is out of adjustment or it already IS configured as a left-handed mouse. If the left button only sends commands on the second click, that would be my first guess. If commands are sent by a single click of the RIGHT button, then it's a configuration issue. Go to your Control Panel and configure it to a right-handed mouse.
Actually there are so many factors that can cause this to happen. Dirty mouse, misconfiguration, sensitivity or just simply bad hardware. First, however, I would try the right button.
A shot in the dark but shut down your computer and unplug the mouse. Reboot. Windows should give you a message saying that there is no mouse attached but safe to install one at that point. Then re attach the mouse and continue booting. On occasion, after extensive use, connections become bad and simply need to be reseated.
If all else fails, (re) install the bundled software or buy a new mouse. But start with the easiest tip, check the other button. :)
Good luck! I'd be interested in your solution to.
Regards,
Jesse