Did you see a little bar pop up and and say something like "downloading google chrome" and then installing?
Go to the start menu, see if you have a new Google Chrome folder under the all programs section.
Now, if you do, you have installed it fine, and can now begin using it after you run thru the short little setup wizard that pops up when you run for the first time after installing.
I would think your fairly new laptop isn't 'joking around' with google chrome browser :LOL
Hope its ok.