[Argus25]

Most likely it was a 4.7 or 10uF 16V Tant and the ripple or peak voltage from your plug-pack exceeded that. Tants do this if over-voltage or reverse polarized, but it cannot have been the latter as it was running when it failed.

It looks like there are 0.1uF bypass caps in the region. You could replace it with a 10uF 35V Tant to prevent this in future, these have a higher ESR than a 16V one of the same capacity though, but with the 0.1uF bypass caps there it wouldn't matter.

Likewise a 25V electrolytic would be ok, that is if there are definitely 0.1uF bypass caps on the regulator's input and output to ground. Sometimes if there is not and the capacitors on the regulator input & output are too high ESR, the regulator, probably a 7805, will oscillate.

One helpful thing with devices that run off plug-packs, which are isolated from earth, is to put a small bridge rectifier, like a WO-4, on the power input to the PCB, that way it is also protected from reverse polarity and works with either polarity presented to it by a plug-pack (wallwart). It prevents reverse polarity accidents. An input fuse never hurts too but often they are not there in many designs, one probably would have saved the capacitor from total burn up and the mess you now have to clean up. (A single series schottky rectifier diode works too for a DC output plug-pack, but will only work with the correct polarity).