Think you will find that the blue thing is an inductor (iron ring/loop) to soak up any interference. The black device on it's back! looks to be a relay, and judging by the addition of the wires underneath it's the wrong one hence being up side down and jumpers being used. (bodge repair )Are there any markings on the big blue thing with the wire wrapped around it or the 8 legged black thing that's been glued in with a glue gun?
YepIf the output from the small (40 to 13v) transformer goes through a rectifier would an easy test be to simply connect 12v to it (via the blue wires)? Surely the polarity couldn't be wrong as it'd be before the rectifier and it would power up the 12v side of things? Mind, I can't see a rectifier myself unless I'm missing something.
Ah, having just followed the blue wires onto the board it connects to the little roundish black device next to the plug which has 'W04G' and '140C' plus a couple of squiggles that indicate AC. It also has 4 contacts, leaving me thinking it is a bridge rectifier?