Hi
"Well, I tried converting the AVI into an MPEG2 and, for some reason, it also gets rid of the sound when
I put into the timeline into VP"
No idea why that happens. 
When you load the converted file into VP is there an audio track displayed? (ie peaks)?
If its a one off problem which you are not going to encounter a lot then you could try this...
Load your original avi clip into the VP media list. (The one that plays slow) and then right click it on the list and select "save audio track". A copy of the audio will appear on the media list.
Now add your MPEG2 conversion to the list and drag it to the sequence line.
Drag the saved avi soundtrack down to Soundtrack 1 line.
Right click the video clip on the sequence line and unlink its sound. This will drop down to Soundtrack 2.
Now LEFT click this soundtrack to nudge it slightly and then RIGHT click the track and choose "Remove the selected audio"
This should leave your MPEG2 clip with the soundtrack from the original avi clip. You may need to then juggle about a bit with the position (or the video speed) to get it into precise synchronisation.
Worth a try anyway.
Nat