Manual WordPress Update Problem

I’ve had some major issues with the installation of 3.9.1 and cannot use my dashboard. It was suggested that I manually update wordpress. I’ve downloaded the latest zip of WordPress and I’m reading the “Famous 5-Minute Install” which seems to be taking a lot longer than 5 minutes!
So far, here are my questions:

1) It says to upload the new wordpress package…where am I supposed to upload?
2)The wp-admin/install.php that I’m supposed to put in my browser doesn’t seem to actually do anything. What is step number two telling me to do? I get a message saying I’ve already installed WordPress. It says I have to clear all my old databases. I don’t have a clue how to do that, plus I don’t want to lose everything I have.

My host is Host Gator. Should I just contact them?