MacBook – What does “A1278” mean in specifying a MacBook model

This is hard to guess, as you can imagine. If the machine had kernel panics the usual (but not only) suspects are RAM chips. You can probably try new RAM (google for OWC, CRUCIAL, etc.). The battery can be replaced at an Apple Store (of course you'll have to pay for it). The Hard Drive could be a problem too, so maybe if you had to replace it, adding an SSD instead would boost the performance.

In the end, there's little else you can replace without having to ditch the entire motherboard, and that's probably not worth the cost outside the warranty.

Running a Linux (more tolerant sometimes with dubious RAM/Hardware in general) is a decent alternative. Ubuntu (among others) is a decent OS for casual users.

It's likely that the controller for the trackpad and keyboard (I believe it's one chip for both) is dead. I had an issue where the keyboard and trackpad on an older pre-unibody model would become non-responsive, but the rest of the top case components were fine (power button, back light). It was tracked to a faulty controller in the top case, but the solution was to replace the whole thing.

iFixit sells replacement top cases, but they're rather pricey ($299.95 for the A1260-compatible part). You might be able to find a cheaper one used on Ebay or elsewhere. The repair itself is fairly straightforward.

Have you tried plugging in a USB mouse or keyboard yet? If the problem is what I think it is, that should work fine.