The corrosion compounds can conduct electricity, and will be specially bad on higher voltage areas.
Thus, the mosfet gate and its driver could have been exposed to the motor voltages.
When there's corrosion on the pcb, no amount of alcohol will fully remove it, IPA it's a solvent, solvents don't dissolve metals, neither oxides, yeah you'll give a nice brushing, it's the mechanic action what removed it, but still you'll never remove all of it that way.
I always remove (desolder) the parts, then fully renew the solder on the traces so the flux makes some work on the corrosion.
That will help, but won't remove all of it, so pass a desoldering wick to remove all of the new solder, clean with ipa, then give a light brushing or fine sanding (I said light, with a small brass or glass fiber brush, or a grain 1000 sandpaper) to fully clean the area until you see shiny copper or tin.
Another IPA cleaning, now make some connectivity tests ensuring all traces are ok.
Take care of any color change on the solder mask (darker/lighter colour), expose the copper on those areas with the brush, as that's usually a sign of corrosion, some traces might look ok but be completely corroded under it.
Fix any damaged tracks, re-tin the traces/pads.
Also do the same with the removed parts if still in good enough condition.
Then put everything back together, again make continuity tests before applying any power.
If you got it working, apply some coating to protect the repair areas. Nail laquer is usually a cheapo and simple way.
If often exposed to humidity, better to apply some type of silicone.