I think it's either one of two things. First the main power amp is faulty. In smaller systems this can often be done by a single IC power amp. You can check this by looking on the heat sink and see if you can see a multi pin device attached to it. It might have the letters STK on it. If you put the letters and any numbers found on this device into Google, you can see how much they cost!
The other possibility is the volume control IC is faulty. If they sound goes up at all, even though very weak, I would put more money on it being an output problem than anything else. One thing is certain the pre-amp section is working, which is why you can hear sound! It's just not getting fully amplified.