Shutting down during startup, possible keyboard malfunction?

I know this is a common problem, with many other questions on here pertaining to Macbook Pro's that shut down while booting up. But in this situation, there is an interesting twist that seems a bit more uncommon. It seems if while booting up, I hold down any key continuously, the machine boots up and stays running. However, if I do not hold down a key, it will shut down after 10-30 seconds. Or if I release the key after a few minutes, then it shuts off. I've been trying to install OS X on a drive, but with it shutting down during install, it's a challenge. Is it possible that something with the keyboard is causing the issue? Would replacing the keyboard potentially fix the boot up problem? Seems weird, as the keyboard is working (in that I can type, hit command key combos and such). But like I said, if I hold a key down it will boot and stay running, but with no key held down, the system will shut itself down. Hoping there's some short or something being caused by the keyboard, and that the problem isn't a faulty logic board. Anyone have any experience with this same kind of issue?