Unshakable Infection

I acquired a computer virus the other day. I have no idea how it took over my machine. I'm careful to the point of paranoia and update my computer's security all the time. I never fall for the 'click on this link' or the fake landing pages that ask you to reenter your password for Facebook or Gmail. Despite all the best laid plans, I'm at the mercy of some bug that's crushed my computer and seeks to steal my bank account information and passwords to my sites. The problem is that I know just enough to know that I have no idea what I'm doing when I'm trying to get rid of it. I look at the processes that are running and recognize about half of them, but I know that most of the other half are things that run in the background I just never notice. I've begun randomly deleting things to see if it helps. It's the same method we employed when rewiring the shop at my old job. We just started cutting things and seeing what turned off. That method worked alright. Or, at least nothing burned down.