Advice on converting video files -- why do they come out with audio/video not synced?

I’m trying to convert some movies to put on my sister’s iPod (avi to mp4). The original files have audio/video synced perfectly. In addition, some movies converted fine, but certain ones refuse to convert nicely.

It may be related, but I’ve never been able to burn movies to a DVD player format due to this same issue. I even tried several different programs and the outcome was the same, unsynced audio/video.

My computer isn’t new, but it should be fast enough.. dual core processors, 2 gig RAM, and I also shut down all programs while doing video conversion, including internet and anti-virus program.

Does anyone know why this is happening? Any suggestions for system settings, or a different program, or anything? It’s very frustrating.