This is bad. But don't throw it away, this can be fixed. If you don't have the skills now, you might later on.
What this board needs:
- remove anything that's not soldered down (cache, CPU, jumpers.)
- desolder that battery whatever you are going to do
- wash the board with white vinegar, scrubbing hard with an old toothbrush - then rinse with water (demineralized if your water is hard)
If you're extremely lucky this will be enough to get it working, but I strongly doubt it given the extensive leakage.
Next steps:
- de-solder all components in area affected by the battery leakage.
- clean those components and test where possible (resistors, capacitors and - if you have a TL866 programmer or similar - the 74 and 40 logic chips). If not possible, assume dead.
- clean the now depopulated board again thoroughly with vinegar.
- check connectivity on the affected traces.
- if traces are broken, bridge the damage with bodge wires.
- procure replacement parts for anything that was dead or could not easily be tested (that keyboard controller...)
- solder it all back together and test the result
Here a very good step-by-step video showing fixing similar damage on a 286 board: https://youtu.be/XdT0byPMnZY?si=eL7GqS1cEPCFYAUy
(in fact, watch every one of Necroware's videos - even if he's messing around with very different stuff, he shows the techniques he uses clearly in every video and they can be applied to pretty much anything and I've found them invaluable)
To do something like this successfully you need good tools - above all some way to reliably and safely de-solder complex components. Old-timers will say it can be done with copper braid and some good flux, and that is technically true, but I'd thoroughly recommend a de-soldering iron/station given the number of pins we're talking about here. Apart from that, some fine wire, some leaded solder, some good flux and a fairly small soldering iron. In terms of testing, a multimeter that can measure resistance and voltages is a must. If it can do capacitors and transistors so much the better. I swear by my TL866 EEPROM flasher, both for reading flashing EEPROMs (like BIOS) but also testing SRAM (cache) and small (74) logic chips. Finally an oscilloscope is handy for things like checking whether oscillator crystals are doing what they are supposed to and whether correct clock signals are getting to CPU and other places. It can also help to reverse-engineer jumper settings on hardware without documentation (not a problem you will have with this Asus beauty). That said, a good scope is expensive and/or hard to come by and is probably the least essential thing in this list.