How to tell why it wont attempt to turn on

What are the symptoms you're seeing? What does it do (if anything) when you attempt to power it on? Have you tried resetting the PMU/SMC and PRAM? Have you removed the battery, reseated the RAM, and tried a known-good AC adapter? What color is the light on the AC adapter?

Again, it all depends on the symptoms, but the DC-in/sound card (i/o board) controls power functions, so when that is having problems, the symptoms tend to be power related. If the computer basically works, but power-related functions are acting funky, there's a pretty good chance the DC-in is the problem. However, since the logic board and the DC-in are tightly integrated and the logic board "sits behind" the the DC-in, so to speak, it's often very difficult to know whether it's the DC-in or the logic board, especially when the computer is not responding at all. Often the best first step is to replace the DC-in, because it's by far the cheaper of the two components, and see if that changes anything. If the computer works at that point, you know the DC-in was the problem, and if it still doesn't, you know the logic board is the problem.

But let us know what you're seeing, because knowing what's going on with the machine will likely make all the difference.