Well, something is wrong with your WP install then. As a second option, in the right pane, at the very top, next to the large word Plugins should be a button that says Add New. Is that there?
If not, are you using any plugins that affect the Admin/Dashboard part of WordPress? I suggest you disable all your plugins and see if that resolves the issue. Then turn them on one by one, refreshing after each, and see if one of them causes the Add New option to disappear.
If that doesn't resolve it, temporarily switch to the default twenty ten theme and see if that resolves the issue. If it does its a problem with your theme.
If it doesn't resolve it the next thing I'd try is manually uploading all the WordPress files again, in case any of them are missing or corrupted.
You could try switching to the 2010 theme first, since its easier, and see if the problem is resolved. And then disable your plugins one by one with the 2010 theme active, to locate a problem plugin.