dont worry about ground for now.
I see the capacitors effectively not connected on one side
but tied together on the other
View attachment 239892
so all they do is tie together those two black and one white wires that go someplace else.
With one side floating they're electrically "not there".If this is just a plaything
you might be able to figure out which of those burnt up wires goes with which
splice them by soldering into each a splice of similar sized copper wire between the loose ends
than soak the whole area with varnish or high temperature paint.
I've had good luck with woodworker's polyurethane varnish
and with engine enamel from the auto parts store.
It's cheap, takes an hour or two to prepare and solder the burnt wires
and works for me about half the time.
If there's insulation failed back inside the stator where you can't see it you'll have to rewind
but I've fixed appliance motors, a drill press motor and an automobile starter that way.
Good Luck
and have fun !
old jim