Ever heard of 'The Capacitor Plague?' I think I see where junk leaked onto your board, one sign there could be such a problem, though I thought it was supposed to be all high voltage/radiation capacitors having the problem. Haven't heard of ebikes being affected, but then maybe there weren't enough then to create the discussion. Obviously the controller is still working if you're just looking it over. When these things fail altogether there's spectacular visuals.
You might remember there was maybe a decade of not very old big screen TV's put at the curb and people saying they fixed one for $10. There's the problem I'm talking about. Most famous problem was all the computers that would freeze, reboot suddenly, etc. Dell paid a $300 million plus class action suit. Just a guess, can't really see in the pic. But I'd say figure out a model number for any of those cans you think might have a problem and you could discover 'Yep, that's a capacitor.'
Or maybe a replacement is cheap. That Clean Republic Sprinter 10K Samsung Li-ion battery pack is supposed to be airline friendly.
http://endless-sphere.com/forums/viewtopic.php?f=3&t=22444