I have since done some more troubleshooting from a clean install, and the issue is directly related to the Audigy DOS drivers. However, I found that if I start Windows 98 with the command prompt only in the F8 menu, the sound card initializes fine. I do not know why it would work fine there and not when I shut down the computer. I know that autoexec.bat runs on startup, and I don't get any error messages when I start Windows 98, so the sound card initializes fine upon booting and works fine whenever I go into a command prompt window within Windows 98. I'm not very familiar with the shutdown process of Windows 98 to understand why it would try to initialize again and fail when rebooting into MS-DOS mode though.

I have also tried multiple versions of the DOS drivers (the Sound Blaster 16 emulation driver) and have experienced no difference.

Is this one of the motherboards that has the onboard AudioPCI64 soundcards?
If it is is it disabled? Maybe its conflicting as the onboard uses almost identical drivers to the Audigy.
just a guess

Yes it is, and I did disable the onboard sound in the BIOS.

So, I installed a different version of the Audigy DOS driver from the Vogons Drivers website, and what happened was interesting. The problem still persisted if I shut down the computer, but the DOS driver installation edited the exit to DOS .pif file to load separate autoexec.bat and config.sys files. This leads me to believe that this was a known issue when these cards were new, and this is how Creative Labs got around it to ensure everything would work correctly.

So my solution ended up becoming more of a workaround. I noticed that the only thing in Autoexec.bat file was loading and initializing the Sound Blaster 16 emulation driver for DOS, so I renamed it and added that to run in the batch file field of the exit to DOS .pif file, so it only initializes when I restart into MS-DOS mode now. This works out because this is also the most efficient way I have found to load mouse and CD-ROM drivers in MS-DOS mode under Windows 98.

Yes that's what I found as well. Keep windows and dos startup files as separate as possible.
Even back in the late 90's I created a shortcut on my desktop, not even using the option in the windows shutdown menu.

This was on my GP6 400 and using the onboard and later SBLive! driver, so your work around is even period correct 😀

I do like to keep my projects period correct 😃. I can always copy the file from the Windows directory to my desktop and do it that way as well!