The mainboard works by routing data between devices. As far as I know, there is no specific "channel" on the board dedicated to sound (other than those in a sound card or integrated sound circuit). If the computer still starts up correctly and is simply not outputting sound, adding in a separate sound-card will probably fix your problem. A board incapable of routing data correctly would not POST.
A standard PCI sound card is cheap, usually provides better sound quality (isolation from the mainboard reduces cross-talk), higher volume, and even adds a tiny amount of performance by isolating sound processing from the CPU. Don't worry about the extra ports on a card. They are all configurable to use a single line-out and will work fine without one of those fancy expensive speaker systems.
This one has great ratings and is under $10!
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Whoops.. just search Newegg. cheapest sound card listed and it looks like a winner for you.