Hmm, I wouldn't have thought that damage there would have stopped the board starting altogether. That's the section that interfaces with peripherals so it should start to post and then beep like a news station interviewing drunk granny at Christmas.
What I do notice though is there appears to be damage inside the ISA slot, and the pins for the nearby IC also look corroded. While this is fixable, tread carefully. There are a few good sources about restoring traces if you want to go down that route, or bypassing them with thin wires and soldering if you prefer to go that way.
First thing you want to do i'd hazard is get a pencil with an eraser on the end, and use the eraser to try to clean up the traces to see what's corrosion, and what's just discolouration.
I expect the reason it's not booting is you haven't replaced the battery.