I am having the same problem. I cannot install Core Plugin. However, the Revolution Slider apparently works in my case.
I also cannot see Services, Portfolio or Team Members in the admin panel and I am not able to see shortcodes on Pages or Posts. Is this related to the missing Core Plugin?
I am on the latest version of WordPress, but I also tried installing an earlier version of WordPress (3.6) to see if the problem was related to compatibility between the theme and the version af WP, but no luck.
Look forward to your reply!