Well the first thing doesn't make sense.
If you can just pull the movie right off the memory stick, then by playing it you hear video and sound, and it's in an mpeg format, final cut should read it.
Now, if it uses a codec that it doesn't recognize that'll cause a problem. I'd look in quick time under the movie properties, to see what the video and audio track are encoded with. Now the reality is that if it were encoded with a codec that FCP didn't recognize your version of quicktime wouldn't recognize it as well.
FCP's movie architecture is based off of your quicktime player. They go hand in hand, if one won't read something the other won't.
If you really want to try and convert the file to another format, just make the video and audio compressors "none."
But it sounds like you're just doing something wrong with final cut that you can't hear any audio.
*A thought, if you drag the clip from your project bin to the viewer, then take that entire clip and drag from the viewer to the timeline. If you look at the audio levels on the right side, do they move and you still don't hear sound?
If that were the case, your playback device isn't set correctly. You'll have to check your global sound settings. Then in final cut, check by going to audio video settings, and look at the audio playback tab, and on the first page you come to, at the bottom there's a pull down menu, which talks about what device you are using for sound.
Everything needs to be play on desktop, use built-in audio, etc...you don't want it to be using firewire playback.
That's all i can think of bud...