Logic Board Change to Core Duo 2

I have a Black Macbook Core Duo that I've been constantly fixing. It's last accident involved water. I cleaned the logic board up with 90% pure alcohol, left it to dry over the weekend and got it to start up and log in, only problem was that it would only do so if the battery was out and the AC charger was connected.

After a few trials it just wouldn't turn back on, no matter if the battery was out.

It's last sign of life was turning on but no chime and no screen signal... it won't turn on since then.

The battery charges if I connect the AC charger to the laptop and it goes all the way to a full charge, the light on the AC charger also turns on.

My guess is the logic board died so I looked up a used logic board for this model (its a MA701LL/A as far as I can tell, with a 4 wall thermal sensors) but not even ifixit has it on stock, all I keep on getting is 2.2GHz and up.

Would one of those 2.2GHz or 2.4GHz logic boards fit my macbook?

Thanks for your help!