If you're in a space craft (theoretically) travelling JUST under the speed of light, and you run from the back to the front of the spacecraft (enough to make up the difference from space craft speed to the speed of light),
Three things happen as you approach the speed of light:
1. You get heavier
2. Time slows down
3. You get foreshortened in the direction of travel
In other words, you won't have anywhere to run.
Also, of course, the speed of light is a constant for all observers, yadda, yadda, yadda...
QDM