In looking at your logic board pictures on the first page, that's some serious oxidation/rust.
It would be a good idea to soak the board in vinegar, or use an ultrasonic cleaner with detergent specifically for electronics, to stop that corrosion.
The pictures appear to show broken traces on the top and the bottom of the board and possibly rotted capacitors but it's hard to tell without a continuity check, or from just a picture.
The only schematic I found for the SE was here:
Apple Macintosh - Apple and Bomarc schematics for Portable, Plus, SE, SE30, Classic, II, IIci, IIcx, IIfx, IIsi, LC II, LC III, Quadra 840av.
oldcrap.org
-And they are fuzzy looking .gif files.
I'm not much help but contributing what I can. Can only recommend to use a magnifying glass/headset to spot what looks like dark spots interrupting the green traces on the chip legs, or caps, and then verify the traces with a meter.