Give it a try! It might work badly, but probably won't fry the stereo. Pick one that doesn't need a minimum load on the 3.3 and 5 volt outputs, and stay away from the cheapest models. Do not attach one of those giant car stereo capacitors: it might make the power supply oscillate, and it's pointless because the power supply doesn't droop like a car battery does.
What's with all the bad information? Good modern PC power supplies are strong. Last year I put one in a laboratory instrument driving a 12 V, 0.5 ohm heater controlled by an audio-frequency PWM. It didn't break a sweat, and saved loads of money over a "proper" supply. As an example, the Enermax EG851AX-VH(W) can put out 28 amps on its puniest 12 volt rail. Depending on its internal construction, you might be able to parallel the 12 volt outputs to get 38 amps total.
"switched power supplies like a pc one, will produce much noise in the audio band, because of the current switching."
The modern ones switch way above the audio band. If noise turns out to be a problem, a choke and capacitor should take care of it.
"PC power supplies typically will output a lot of power on their 3.3V and 5v outputs, but the 12v outputs is a lot less as there are not that many things that use 12v in a PC."
On modern supplies the 12 V rail is by far the stoutest. It's just not practical to run a pair of 130 W processors on 3.3 V: the needed wires are too thick. The processors, video, and motors all run on 12 V, and often the memory and chipset do too.
"pc supplies are not intended to withstand for extreme current requirements like a bass sound,"
They most certainly are. Consider a game that has 50% utilization with a 100 Hz frame rate, running on a pair of 100 W CPUs and a pair of 50 W video cards. The PS would easily see a 100 Hz, 250 W square wave load on its 12 V rail.
"60 watts at 12 Volts equals 21 Amps, much more than any PC power supply will supply (more like one Amp at 12 V)."
If you have money to burn and reliability isn't a worry, there are units that go up to 72 A.