Top Case/Keyboard Trouble

I've been having a major problem with my Macbook the two weeks. Two weeks ago, I spilled a little bit of water on the keyboard. This has happened before, and it was not that much, so I thought nothing of it. The next morning, the mac was typing in random keys by itself, so I shut it off. Then, it wouldn't turn back on. But after removing the top case and plugging it back in with the power on, it powered up. I assumed, correctly, that the top case was the problem. So I ordered a used one on eBay. It worked perfectly except for one key. So the guy I bought it from sent me a different one. Now, one of two things will happen: either the light in front turns on, blinks for two seconds, beeps for another two seconds, then starts up, getting to the log in screen, then the whole laptop powers off. The second thing that sometimes happens is that it starts up right away, then powers off right away. I was so afraid that my logic board was fried, but when I plugged my original top case in to see if anything happened, the mac started up perfectly, I just couldn't use the keyboard or mouse. Any help would be greatly appreciated as I am pulling my hair out here trying to get this to work. Also, if anyone could tell me a way to power on the macbook without the top case, I would really appreciate it. I also want to note that when it turns on then off, if i quickly pull out the top case, the MacBook starts up.