How far did you follow the corroded traces to test them? (continuity test, I assume) Multimeter or logic probe?
I've got some non-working boards that have corroded but intact traces, but I highly suspect there's broken contact between one or more inter-layer jumper trace bridges. (or whatever those are called: the tiny holes in the board jumping a trace from one side to the other of a PCB)
I haven't attempted repairs of these yet, but I assume it'll involve cleaning out those jumper holes and patching them with solder and/or a copper wire strand + solder.
Any un-broken jumpers will probably get damaged in the cleaning process anyway, so I'll have to fill any one I mess with. (aside from any I can surface-clean well enough to test on both sides of the board)
Those sort of jumpers are also often connected to tiny, almost hair-thin traces, sometimes closely grouped together, so not fun to have to fix. (especially without an advanced solder station, magnifying glass, clamps/clips, etc and a very fine, sharp-pointed soldering iron tip, or wedge/blade tip with very square, sharp corners)