Ok, that means you have a working sound chip, but no connection between the chip and the speaker. I can't tell where it's broken from here. If you can identify the Realtek sound chip, perhaps you can find the data sheet and identify the sound output pin. Then, use a scope to see if it's putting out any sound at the chip. If there's sound at the chip, but not at the output connector, you have a motherboard with a possible broken trace, blown audio amp (if present), or broken coupling cazapitor.
Ooops. I forgot that it default to the timer sound output instead of the sound output. I wrote that in 1985 and my memory is becoming rather ummm.... dynamic.
Some motherboard run the PC speaker audio through the sound card. Apparently, this one does not. So much for that idea.
I'll keep looking for some DOS based diagnostics with a sound test. It may have to wait until I drag myself to my palatial office sometime next week.
You might find something useful under this review: (9 pages) This might be a diversion but could be causing the sound to be muted: Viiv support (i.e. support for Quick Resume technology, which allows the PC to imitate the behavior of TV sets, where by pressing the power button located on the remote control the screen goes dark, the sound is muted and the keyboard and mouse stop responding)"
Bingo. It's a Realtek ALC888 sound chip. Digging...
Data sheet link is at the bottom of the page. Section 6.2 shows front audio outputs on pins 35 and 36. Dust off the oscilloscope and see if there's any sound on those pins.