Hi, On the lower picture of the blown capacitor, (I pretty sure that is what it is) I can just make out on the bottom edge of the capacitor, something "uF" If you can see what is written in front of that we will have the value of the capacitor in microFarads. Also given that the cap shown next to it has a voltage working value of 25V there is a fair chance that the blown cap will have the same voltage rating. i.e. xx uF, 25VW, -40 +105C low esr.
If you have an Ohmmeter connect across the two pcb board connection points of the cap and see if there is a low reading. Reverse your meter leads to check the readings 'both ways'. It may be that you get a low reading with the meter leads in one direction but hopefully not in both directions as this would indicate a s/c somewhere. In one direction only may be OK as you may be looking at a diode or other type of semi conductor device.
If you do find the value written and can find replacement part online order 2-3 as if you replace it and it 'goes again' due to more problems further into the circuit then at least you have a spare handy once you have found the problem.
Also just wondering, you said it worked on a 3V charger. Was this a negative input or positive input charger, i.e. -ve leg on centre pole of plug. If it is a positive input then 25VW caps seems extravagant by the maker as there are 16VW ones. Just a thought.
Not good news I'm afraid. It means that something else has 'blown' in the circuit. Check for evidence of heat stress or cracking in the IC type of components close to where the capacitor was located.
Here is an image to give you an example. It is NOT of your particular circuit
Imagine that C1 is your faulty capacitor. With the Ohmmeter across its' connections in one direction you may get a reading thru the path of C1 > IC1 3-1 > R2 >R5 >R1 and back to C1 when you have the leads in that direction and when you reverse the leads because IC1 is now 'dioded' there should be no path thru IC1 1-3, or at least it should be a very much higher resistance reading than the other way. There should also be no path through C2, Q1 or IC1 3-2 or C3 BUT because the 1st path mentioned before is in parallel with these components it is a bit hard to tell without isolating parts of the circuit.
Essentially what I am saying is that there most probably is a voltage regulator in your particular circuit that has gone s/c (short circuit) that is why you are getting the same reading in both directions. One way to find the problem is to start at one of the capacitor connections and trace the track to the next component, remove the one leg of that component from the board and then measure again to see if it still measures the same in both directions. If the track 'finishes' at a component, it means that the circuit continues through that component. If it is a regulator IC (i.e. not a capacitor or resistor or mostly anything with two 'legs' - I know diodes only have two legs) then you have to remove it and test between the usually three 'legs' e.g. in the example of IC1 you should read low resistance between 3-1 and 1-2 but not between 3-2 and also not when you reverse the meter to read between 1-3 and 2-1 and 2-3.
Alternatively the quick way is to remove each regulator type IC, close to the failed capacitor location from the board and measure it out of circuit to see whether it is OK or not. if you find a faulty one that still doesn't mean that that is the only problem as other components may have failed as well but it is a start as you can then look at the other components directly associated with the 'failed' regulator (it that is what it the problem) and check them as well rather than having to go through the entire circuit.
So good luck and unless there happens to be a circuit number printed on the board that you can use to find the circuit online to make it easier to fault find, then "Welcome to the world of fault diagnosis and repair at component level in electronic circuits without the aid of a circuit diagram".