Looks like a LCD cable fault inside the machine. I haven't had my hands inside an imac so unsure how they deal with video to monitor exactly, but had this same issue on a Dell Laptop not long ago and it was a loose/faulty LCD to Gfx card cable (that particular instance was a ribbon-type cable).
Gfx card would be OK as remote screen sharing is working (as all the processing is still done on the host machines video card). Your System profiler shows theres nothing connected to the Gfx Card under the Display Connector area. Check the System Profiler once the monitor is working (that should confirm or blow out my theory).
Websites such as iFixIt should guide you through taking apart/checking the internals of an iMac (Linky > http://www.ifixit.com/Browse/iMac_Intel