You can use any brand of capacitor. You will need the same pin spacing and diameter. You may be able to use longer capacitors if you have space.
The voltage rating and temperature rating should be the same or larger. The capacitance can be larger as well. In that application, the bigger the better.
The item D2 is the bridge rectifier. The two centre pins are connected to the mains (via noise filters and a fuse) and the two outer pins charge the capacitors.
The two capacitors are in series. That is done so that they can be charged in series with 240 V mains and separately with 120 V mains, giving the same voltage across the two capacitors for either supply voltage, as long as the selector switch is in the right place. The damage shown could simply be that the switch was set wrong once.
There should be a pair of balancing resistors, one in parallel with each capacitor. It's worth checking that those are working. If not, you will get a bigger voltage on one and then it will fail.