It could be a blown capacitor. I am not sure how these things go bad, but two of my friends had the same problem recently. One had a Cerwin-Vega sub and the other was an Infinity.
Was it in use at the time and if so was it working hard? Is it hooked up through a surge protector? Were there any power surges or electrical storms in your area before or during the incident?
Amplifiers have parts that wear out over time, sometimes spectacularly. George is right, a capacitor could have easily worn out and blown. When that happens, you often hear a "pop" of the casing of the capacitor coming apart, followed by smoke and the smell of burnt electronics.
There are several reasons for something like this to fail. Often they just wear out, but age, heat, load and prior manufacturing defects can all play a role.
If indeed this is the problem, fixing it requires a screwdriver, a soldering iron, a local electronics parts store (probably better featured than a typical Radio Shack) and patience. If you aren't good with solder, you could send it to Sony for repair. But weigh the cost of getting it fixed against getting a new one. You can probably get a new one that is better than your current one for $500 or so.
Here's the thing - electronic devices run on magic smoke. As long as they have the smoke inside 'em, they'll work just fine. But if you let the smoke out for some reason, well, they quit working.