What is the Audio CODEC?
That WMP can play it, indicates that the necessary CODEC is installed on your system, as WMP, unlike some players, does not contain any CODEC's of its own.
While it could be that it's an Audio CODEC, that PrPro cannot deal properly with, my first guess would be that something else is going on. Still, knowing what the Audio CODEC is, might answer the question.
In a worst-case, you can rip the Audio, Save that as a PCM/WAV @ 48KHz 16-bit file, and Import that, for use in editing.
Also, after Import, did you allow Conforming to complete 100%. The creation of the CFA & PEK (Waveform Display) files is very, very important.
Did you import the COMPLETE BPAV directory? It is not enough to import only the MP4 files.
In the Project panel, do the clips appear as video only (filmstrip icon) or as movie clips (filmstrip and speaker icon)?
Dazed and confused here... I've figured out that the audio is recorded on four separate tracks, but I can not get Adobe to recognize the other audio layers of the file. We have imported the complete folder, but to no avail. I've created four mono audio tracks, but still get nothing. When I go to modify the audio channels, it lists only one channel.
Doh. Nevermind... just re-read your post
Have you tried using XDCAM Browser from Sony to rewrap these into MXF files?