Please forgive my crappy drawing, which my roommate is making fun of as I type this. Here's the problem with normalization: 

You can see that the overall waveform has relatively low amplitude - except that really huge, (time duration) short spike on the left. Since normalization uses that spike as the "standard" 0db volume level and since it's already maxed out, normalization will do nothing for you. What you need to do is lower the transient spike. How do you do that?

Compression. Actually since the time value (across the x-axis) is very small, you would use limiting instead, which is like compression on steroids. Once you bring down the two transients spikes on the far left and far right, you can bring up the total volume of the audio.

Soooooooo once your audio level is brought up, your noise floor will increase. So you will need a noise gate to eliminate the new, louder noise. Once you apply it, you will have Hollywood-quality sound.