I am pretty sure it wouldnt. I mean the firing device is like an independent variable. It does not matter if a gun is stationary or moving. The speed of a bullet fired from the gun is not going to increase or decrease if fired from a bus rite? So if you were to fire a cannon at the speed of light from the front of your ship it would always remain just slightly ahead of the ship. The bullet is going at the speed of light and so is the ship. The bullet is not compounding any extra speed from the ship. Get it?
If it's the question R0ckets03 quoted above, then no. This is a "velocity addition" problem. Logically speaking, yes, the velocity would be the speed of light + the speed of the hurled ball. But this is only true in Newtonian models. This is where, like I said earlier, Newtonian models tend to be skewed/fail at relativistic speeds. It's one of the reasons that the Special Theory of Relativity is needed to explain this (also do a search for Lorentz transformations). The ball would not go faster than the speed of light. Somebody correct me if I'm wrong... R0ckets03, assume there are 2 escalators going up at the same velocity and we're each on one. If I walk up the escalator while it's going up, but you stand still while it's going up, who gets to the top faster? If I fire a bullet while traveling on a ship, the velocity of the bullet is the velocity of the bullet + that of the ship. But this addition won't work at relativistic speeds.
Kaku is very good. Anyway, if I recall correctly, Einstein's theories say that you cannot approach the speed of light but say nothing about actually exceeding it. Also, realize that time is not such a concrete construct (i.e. not as linear and reliable) as our temporal minds would lead you to believe; its just another dimension in the 4 that we can perceive. E.g., it can be totally warped by gravity. Traveling faster than the speed of light: http://www.cnn.com/2000/TECH/space/07/20/speed.of.light.ap/.
What would happen if you fired a bullet that goes at the speed of light inside a ship going at the speed of light? I mean would the bullet ever catch up the walls of the ship, or would it just hang in midair?