Word Press not upgrading

I’m taking back over a website after a hiatus and am having trouble. version 2.7.1 is installed. when I go to tools to upgrade to 3.5, I get a message that says:
“You have the latest version of WordPress. You do not need to upgrade. However, if you want to re-install version –, you can do so automatically or download the package and re-install manually:”

There is a download button (which I would like to do since I don’t have these files on my machine as a backup), but when I click it, nothing happens.

I need the upgrade so I can install some new plugins that we need on our site!