Why does my MacBook shut down after it boots up?

I bought this late 2008 MacBook on Ebay about one month ago. It worked just fine until four days ago when it started shutting down soon after it booted up. I had it checked and was told I need to replace the top case and track pad because the power button is sticking and signaling a shutdown. If that's so, can't I just fix the power button or does the top case and track pad really need to be replaced?