Hi. August 2012. My 21 inch 1 year old iMac is doing this. I am using two displays, and the external one works just fine, allowing me to do a hardware check. My computer does not recognize its internal monitor. I think it could be a bad video card or connection to or from the video card. At the time, when I felt the exhaust ports, things were hot.
I am disappointed that no Apple response has been posted, nor has anyone posted a solution related to an Apple repair.
Has anyone found that a good vacuuming has helped, or anything else?
If an Apple person is reading this, you might be interested to know that I have been an Apple person since the IIe - while using and creating various DOS and Windws based networks and computers over the years, and that this iMac (which in itself was a replacement for an iMac that died within three weeks of purchase, and that that one was a replacement for an iMac that was dead right out of the box), is the poorest, worst, most disappointing computer that I have ever owned. I am pretty sure that my next purchase, likely within weeks since my iMac is broken once again, will be a Windows-based PC and not another Apple product.
My home network is totally Mac, I was going to buy an Apple TV, I have one of the last Motorola laptops, and old Mac Mini, and up u til this machine generation have recommended Apple products. No longer.
Same for my phone, and my next tablet.
I am totally fed up with the lack of solution posted by Apple for this problem.