Capacitor failure is a very common problem with small appliances, computer motherboards, DVD players, computer external displays, big screen TVs etc. The manufacturers often use capacitors with a very low voltage rating. The top of the cylindrical capacitors should be flat, but when they fail, they bulge.
If that is the only visual problem, replacing them will likely recover operation of the player.
The capacitors help to keep the supply voltage to the chips smooth and steady. When they fail, they loose capacitance, the voltage variation causes the unit to constantly reset. Quite a common problem.