Can you still select the object if not ,can you create and select another polygon object?
Because you could have (accidentilly) masked polygon surfaces or have your current object in a reference layer.
If none of this is the case it could be an hardwareproblem(card not powerful enough or broken) or maybe the wrong drivers which can cause some(minor) inconvinience.
Last thing you could try is that you first turn on polycount(under display and then it's called objectdetails i believe) and then when having faces selected drag over the object if you have selected anything it will show in the polycount(just look at the numbers, topleft in the viewport)so you can see if it's only a graphical glitch or more.
If it's the latter i think your f*cked and probably be better off reinstalling maya.
Good luck anyway