Have you tried replacing WAS drivers with MME drivers?

Your sound card in on the motherboard. It is probably a RealTek sound card. Look on the bottom right taskbar for RealTek's HD Audio Manager and see what the settings are there.

Also have you tried saving the tracks as a MIDI file? If not try that and see if said MIDI file will play in the media player or in any other player.

FYI - After rereading your initial message this hit me, "Now when I audition the MIDI style in the Style Picker, there is a Yellow MIDI drum track, but when It is played back it is a Green Real Track and that's the only instrument I hear. If I save, close BIAB and restart BIAB, and load the song, I can hear all the MIDI tracks, and my drums are still a Real track." I have had the identical thing happen to me. I have tried to locate the problem but so far no luck. I have even opened the song in the VST and moved all of the MIDI tracks and the drum MIDI track to my DAW and sometimes the MIDI drum track works and sometimes it doesn't. I even have had BiaB loose my audio interface so I had to save file, restart BiaB, load file, and then all is good. Go figure!

Whenever I get something stuck in the back of my throat, I dislodge it by drinking a beer.
It's called the Heineken Maneuver.

64 bit Win 10 Pro, the latest BiaB/RB, Roland Octa-Capture audio interface, a ton of software/hardware