No, you cannot run faster than the speed of light. If it were possible to become faster than the speed at which light has been recorded, the object in question, such as a person would gain considerable mass in doing so. The faster the object, the larger it would become. Albert Einstein made great leaps and bounds when it came to Newton and the laws of physics. He brings it back to relativity.
Everything has a relative term. Light, speed, and movement are all relative things, but they are still limited when it comes to what they can do, and respond. As he explained the methods in which the speed of light was deducted, as well as the limitations on not only physical but practicalities as well. While there are some debates on the theories that Einstein put forward, his calculations bring into focus a great many things.
It is physically impossible to run at the speed of light. The calculated rate for the speed of light is currently at 186,000 miles per second. To move this fast would cause significant harm and death to a human body.