My understanding from working with laptops for a while now is that the processors are soldered onto the logic board, so therefore would be all but impossible to swap out, as the soldering is on pins underneath the processor itself. Even if you were up to the soldering challenge, you would still be limited to a Core 2 Duo processor, since CPUs are designed for specific sockets. The socket on an A1278 logic board would be designed to only accept a Core 2 Duo processor (or another processor from the same socket family). You wouldn't be able to throw an I5 processor in the same socket, however.
I'm not sure how well swapping the logic board for a different one would work either. This issue comes down to fit and component layout (specifically connectors for various components). If the component ad connector layout were the same, so that the new logic board would fit the old case, then I would think swapping logic boards might work (but that is a big if).
Your best bet would be to bite the proverbial bullet and purchase a newer machine with the specs you are looking for.