Replace the board, you are wasting your time.
Capacitors almost NEVER pop like that all by themselves. And if more than one is popped, then you can take the "almost" out of the previous sentence. Something else on the board is shorted out. Don't bother looking for the short, it's probably one of the IC chips arced internally and is putting volts on a circuit where is doesn't belong which is causing the caps to pop.
It's also quite possible your original power supply went bad frying the MB. But the chances that the only components on the MB that went bad were the 6 capacitors that you can visually identify as popped are infinitesimal.
Unless you have the schematics for the board, which you don't have, probably can't get, and wouldn't know how to use if you did, you have no chance of troubleshooting the problem down to the component level.
Unless you just need some soldering practice, in which case have at it. But may I suggest that you buy an AM/FM radio kit instead? At least then your soldering will have some practical purpose.
