Can I take EMC 2242's motherboard and put it in EMC 2121?

I saved a motherboard-blown black Macbook EMC 2121 without HD from the garbage heap recently and followed a guide on iFixit to open it and and removed the dead motherboard. Pretty straight forward. I have a Macbook EMC 2242 which cannot draw power from battery and has a dim screen, and I was wondering if it's motherboard would be compatible with the 2121 before I open it up and try the swap. Can't seem to find a website that would allow me to cross reference the two machines.

Also, if this is possible and I move my hard drive and motherboard over will my Applications still be operational?

THANKS!