Undefined property: Craft\WebApp::$urlManager in /var/www/craft/app/controllers/BaseController.php on line 37
You're probably running PHP v. 7.0 or higher on your DigitalOcean box; Craft CMS didn't have PHP 7.0 compatibility until Craft 2.4.2697, which is why it chokes.

Downgrading your PHP version to 5.6 or 5.4 should resolve your issue.

You should also beware of your MySQL version – Craft 2 has issues on MySQL 5.7; ideally you should make sure your droplet uses 5.6.

And also – I'd look into upgrading the install to the latest and greatest Craft 2.x, if not Craft 3. A lot of good stuff has happened since 2014 ;)