Not all motherboards have a speaker, so a lack of sound might not mean anything.
However if your motherboard does have a speaker, a lack of sound should mean that the PC is working like it should. Which would mean that the monitor is at fault.
My best guess is that it doesn't have a build in speaker, but I have nothing but a picture to base that guess off.
It is always possible that there is a small speaker in the accessory pack that came with your motherboard. It would then be installed in the pins near the start and reset buttons. Check the manual for furthe information.
It is always possible that the monitor has died, but without testing it with the onboard graphics, a graphics card or a different PC I can't really tell-