System specification (CPU, GPU, RAM) would be helpful in order to troubleshoot the issue properly. After Effects crashing on "Initializing Media Core" usually means that the installed third-party plug-ins are causing the crash. Go to C:\Program Files\Adobe\Common\Plug-ins\7.0\MediaCore and remove (or move to a different location to keep a backup) all the files and folders (except dummy.txt).
Well, judging from your screenshot, clearly your system does not meet the system requirements. The resolution is too low and this always implies a weak on-board GPU that won't support AE, anyway. Feel free to fiddle with your graphics driver and settings, but be prepared that it may just never work.