If you travel faster than the speed of light, the beam will shine backwards, which isn't possible therefore you cannot exceed the speed of light. You need to take relativity into consideration. As you approach the speed of light time slows down for the car and everybody in it, everything just works within a reduced timeframe. If for example you are travelling at 80% the speed of light, if you switch on a light within the car then it will appear just fine to everybody within the car. However the beam of light will only travel at 20% the speed of light with reference to it's target so to speak. However the speed of light is a constant and therefore to everybody within the car it appears to move at full speed.
Remember there's two frames of reference - people within the car and a casual observer outside the car watching the scene as it unfolds in front of them (well that's how our physics prof used to tell us to remember it). If you were to travel at 99% the speed of light, the light will still propagate at the constant speed of light, however to the casual observer the light would be travelling at 1% the speed of light relative to the final target (because he sees the speed of the car + the speed of the light - 99%+1%). However due to the reduce time frame, to everybody within the car everything moves at 1% of the normal time (i.e. time that an observer on earth would experience - 1 year to somebody within the car might equate to 99 years to somebody on earth).
Therefore to answer the question, AT the speed of light, the light from the beam will not shine because time in the car would have stopped, and that's where the mathematics appear to break down. This is just a rough explanation, which isn't necessarily 100% accurate but it works for illustrative purposes. However I could go into more detail if you like.
