If you turn on your headlights while driving at the speed of light, what happens?
If you're driving your car at the speed of light and put your headlights on, what happens?
Man, what are you guys in Sausalito on, anyway? As anyone with even the most tenuous grasp of the theory of relativity knows, the speed of light is constant for any inertial observer. Does that answer your question? I didn't think so. Let me put it another way.
Suppose you're zipping down to the Dairy Queen in your Hyundai at 0.99c — in other words, 99 percent of the speed of light. While en route you flip on the high beams and perform various subtle and ingenious experiments I won't describe here. You discover the light from the headlamps is traveling away from you at (surprise!) the speed of light. In other words, your headlights operate normally.
Now suppose a stationary observer at the side of the road performs the same experiment on the same beam of light. She (her name is Myra) discovers that the beam is moving away from her at speed c also. But how can this be, you ask? Since I'm going nearly the S. of L. to start with, shouldn't that give the photons emitted by the headlamps a running start, so to speak, enabling them to travel nearly twice the speed of light with respect to Myra?
Not to put a fine point on it, no. The explanation for this is a little complicated, but the gist of it is this: when your speed approaches c, you and all your measuring sticks become foreshortened, i.e., squished like an accordion along your axis of travel. This throws off all your measurements, making the light beam appear to recede from you at the same speed c no matter how fast you're "really" going. Unfortunately, nobody knows how fast you're "really" going, because in this morally permissive universe, everything's relative. You think I'm moving and you're not? Hey, maybe the truth is you're moving and I'm not. Only God knows, and ip (see column on non-sex-specific pronouns) ain't saying.
No doubt this still leaves a few questions in your mind, but believe me, thousands have been over this ground before, and nobody's poked holes in the theory of relativity yet. For an excellent short treatment of the subject, see Space and Time in Special Relativity by N. David Mermin (1968).