What's inside LED light up shoes? And can they be fixed?

I was sent a pair of LED shoes by a chap called Billy to take a look at. One was working and one wasn't. So here's a complete shred of a shoe that shows how they are put together and how it may be possible to fix simple faults.
I think this may be the first time I've seen a lithium cell potted in resin and also mounted where a user is standing on it!
In hindsight the current limiting resistor for the charging function is probably mounted on the remote two wire charge/control PCB because otherwise the button would short out the charger completely.

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