Windows of the time only included drivers for things required to boot up the system in 32-bit mode, such as for AGP or IDE controllers. The interesting thing is that even if those did not work, 16-bit MS-DOS compatibility mode using BIOS calls would still allow the system to work well enough for you to install the drivers yourself. Audio was not considered essential to boot the system, so you would just have no sound until installing drivers.
According to
the service manual that's an i810 chipset board which uses AC97 audio directly attached to the ICH Southbridge.
That's a software sound card (rather like the Winmodem next to it) where the DSP would be handled by the CPU, using the usual drivers included in Intel's "INF Update Utility." The codec is the digital-to-analog converter which was made by
a number of companies and requires its own chip-specific driver. I suggest looking at page 174 and identifying the chip located at the spot marked AC97 to determine what codec driver to download.
If you can't figure it out, then you could always use a PCI sound card, though note your system may require a low-profile one with a short bracket.