Hi Lancelots and H2SO4, no disrespect intended by me, but you don't understand the special theory of relativity. First of all, the car cannot be travelling at the speed of light relative to an 'intertial observer' (you and I here on earth are close enough to being intertial observers). The car can be travelling at close to the speed of light, say 99.99%, but not actually 'at' the speed of light. For anyone in that car, as long as it is not accelerating, the speed of light relative to the car is unchanged, so the headlights will work as normal.
For observers outside the car, say you and I here on earth, we will see a Lorentz contraction - as the car approaches the speed of light it will appear to contract in the direction it is travelling - i.e. it will look 'squashed'.
It is definitely a mind-bender. The reason you cannot travel at the speed of light is the same reason as to why the speed of light is constant for all intertial observers and also why the car looks squashed. You need to stop thinking in a Newtonian physics paradigm and think in terms of Einsteinian/relativistic physics. Not easy I know!
