You're in good company. That kind of puzzle is exactly what led to Einstein coming up with special relativity. The solution to your puzzle is that at high speeds, you can't just add velocities in the usual way. If send a pea flying at speed v_{pea} out the front of your car moving at speed v_{car}, the equation for its final velocity with respect to a stationary observer is

(v_{pea}+v_{car})/(1+v_{pea}v_{car}/c^{2})

If both v_{pea} and v_{car} are small, then (1+v_{pea}v_{car}/c^{2}) is basically 1, and you recover:

(v_{pea}+v_{car}) for the addition of the velocities. However, if you let v_{pea}=c, then the entire expression simplifies and the final velocity with respect to the stationary observer is still c.