For a laptop there is no hardware or software way to turn them off. Unless you disable them thru the Control Panel. but then you basically turn off yoru sound overall.
I have already explained how this is most likely not a hardware problem when related to laptops. Because of their setup there is no way that they can split the wires like peter suggested. It is jsut not gonna work that way having wires going across a laptop inner area like that.
What stopped working? You say the sound comes out of both your headphones and teh speakers. So it could jsut be that you didnt plug in the headphones far enough to disable the speakers. Could be your headphones jack is coming loose.
There is nothign wrong with checking for updated drivers. But if you go the route via the control panel and turn off the speakers you most likely will turn off all sounds and defeat the purpose. But if you can turn off jsut the speakers and still get sound via the headphones remember to turn the speakers back on when you are done. Wouldnt want you back here saying you are not getting sound out of your speakers.