I have an update regarding the situation. I installed the Sound Blaster 16 Value CT2840 into the computer and got the proper drivers installed, but it had to be done manually. I removed the IRQ 10-15 jumper so it does not conflict with anything using those IRQs. It is fully working in DOS and Windows 98SE. It has a built-in OPL chip rather than CQM.
I have a report about both Doom and Wolfenstein 3D. Doom's performance was still suffering a bit with the AWE64, and when I used the 16 Value, Doom ran even more smoothly. On top of it, Wolfenstein 3D stopped hanging in DOS and has even better sounding music this time. Also, earlier I defragged the smaller of the two hard drives prior to the Sound Blaster 16 Value going in.
Do you think there might be something up with the Sound Blaster AWE64 if Wolfenstein 3D hanged using it but not when using the Sound Blaster 16 Value?