Make sure you CHMOD 777 all folders required by Joomla (in Joomla admin see Help > System Info > Directory Permissions and make sure all are Writable). Then try to install again.

ok I've got it installed as a compnent and a plugin. How do I place it on the front-end? I want it in a module position on my frontpage and I've disabled the login module that came with the template I'm using.

I caught that late thanks, but still when I click on register, it still shows my old registration form not the ajax register form.

AjaxRegister is enabled and I even disabled the mod-login that came with the template (Rocktheme Dominion) and tried another login module, the registration is still going to the other registration form not ajaxregister.

Like I said:

Also make sure that all other 3rd party components / plugins for registration that might conflict are uninstalled.

You have K2 installed which has its own registration component that conflicts with AJAX Register. I unpublished the K2 system plugin and now AJAX Register shows fine.