I have an Akai home theatre system that just went on the blink. Radio channels all display but no sound. The transformer goes nosiy after 2 min, but the supply voltages stay present. The audio amp Ic's does not seem to get hot, as if there is no supply.
Sounds to me like you have a blown amp, or preamp stage in the receiver. Depends on how much money you want to sink into it, you could get a service manual, and start there. In my experience, HTIB systems are rarely worth fixing, as the cost exceeds the price of a new unit VERY quickly. It sounds like you have a multitester, you can check the speaker lines for continuity, and any sort of voltage output to see if you have a damaged amplifier. If the Preamp/input, and Amp stages are on separate PCBs, you can also test for voltage across the two.