Coffee Damaged MacBook Pro Intermittently Powers On Via Power Adaptor

I dumped a whole cup of coffee (with lots of half & half) on my late 2011 MacBook Pro. After I cleaned it up and let it dry, it worked for a few days. Then I powered it down once and the power button wouldn't turn it back on. Yet it still accepts a charge from the power adapter.

I took the bottom panel off and let it air out for a couple more weeks. Here's where it gets weird. I then plugged it back into the wall and it magically booted up and worked like a champ. I then shut it down and again it failed to boot, but still acts like it's charging.

I deduce this to mean:

1. Logic board, RAM, HD, etc. are fine!

2. Battery must have been dead and automatically powers up when connected to power (can anyone confirm this functionality?).

3. The power button or something in that process is fried or has coffee and creamer gumming up the works.

Can anyone suggest what parts I might need replacing?

Thanks!

-J