Have you tried putting it in an ultrasonic cleaner
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i think it'd be useful to isolate the issue and get it working again first. the circuit is simple enough you can test almost everything individually.
are those wet logic gates and diodes working correctly?
Have you tried unsoldering the tiny bridge rectifier DB1 and meter the four diodes within it?
Well I would start of by testing the shit stained components on back bottom right. That looks to be the most significant amount of damage.
Or you can do it the good old read the smoke signals. And force power in to by putting a bigger fuse and letting the part that's fucked burn up and show you the way. But you kina only have one chance at it.
What is the load on the relay?

