if I reinstall the OS then a working version of App Store should come with it then?
Try it. But first, as andyBall_UK has advised, you should trash the existing App Store.app,
Alternatively, use Pacifist (another of andyBall_UK's suggestions).
http://pacifist.en.softonic.com/mac
Pacifist is a shareware application that opens Mac OS X .pkg package files, .dmg disk images, and .zip, .tar, .tar.gz, .tar.bz2, and .xar archives and allows you to extract individual files and folders out of them. This is useful, for instance, if an application which is installed by the operating system becomes damaged and needs to be reinstalled without the hassle of reinstalling all of Mac OS X, (my emphasis)