I would guess that initially you wired the batteries incorrectly.

Remove the damaged capacitor and maybe the board still works.
Replace the capacitor when you get a chance to get a new one.

 

The connections seems to be as designed; however, the bottom two might be a little ambiguous.


The 3 wires do appear to be correctly connected to the board.


Here's one hypothesis. The black tape may have looked OK, but one of the connections to the battery was not OK or was intermittent. Assume that was a connection to the top battery. That would be the same as just attaching the negative supply. However, that may not blow the tantalum (?) capacitor.

Is it possible that you connected anything reversed? Tantalum caps are extremely intolerant to reversed polarity. I have seen them go out instantly in a burst of glory, sometimes with flame.

 

The connections seems to be as designed; however, the bottom two might be a little ambiguous.
View attachment 219715

The 3 wires do appear to be correctly connected to the board.
View attachment 219714

Here's one hypothesis. The black tape may have looked OK, but one of the connections to the battery was not OK or was intermittent. Assume that was a connection to the top battery. That would be the same as just attaching the negative supply. However, that may not blow the tantalum (?) capacitor.

Is it possible that you connected anything reversed? Tantalum caps are extremely intolerant to reversed polarity. I have seen them go out instantly in a burst of glory, sometimes with flame.

Yeah, I thought of that, I may have connected them in reverse. I guess I'll have to be more careful next time, always learning!
Thanks for all the responses, really appreciated them!

 

If you replace the capacitor, it might work. They do act as fuses sometimes.