Chosen Solution
I replaced the HD with a SSD. I now have no screen image or back lighting. Here is where it gets intresting. I took it to Apple and they said it was the screen. They replaced the screen and the LCD cable and it did not work. They said next would be the logic board replacement but they were not sure. Apple just swamps out parts until they find the bad one. So this was just their best guess. Here is some other info. External displays work. Fans are running at 100%. I installed a MC Fan Controller to slow them down and monitor them. The SSD and OSX are running fine.
Lets see if we can first identify what sensor is giving you trouble by running this app: Temperature Gauge Pro. Make sure you remove your MC Fan control application as it could conflict with Temperature Gauge. Post a screen shot for us to see. I suspect your fan problem is due to the fact this model is the first to use Apples enhanced HD’s. Here’s a write up that helps explain things: Apple Further Restricts Upgrade Options on New iMacs. The good news here is OWC created a nice adapter cable which allows you to install other HD’s or SSD’s replacing your current Apple HD. Here’s the needed cable: OWC In-line Digital Thermal Sensor for iMac 2011 Hard Drive Upgrade. The other option here which is what I would recommend is to put the Apple HD back in and then using this dual drive kit you can add the SSD as a second drive mounting it just behind your optical drive. Here’s the needed kit and the following IFIXIT guide to put it in: iMac Intel 27" Mid 2011 Dual Hard Drive Kit & Installing iMac Intel 27" EMC 2429 Dual Hard Drive Kit
Your second issue with a black screen, let you have a working external monitor sounds like the backlight services is having a problem. Using a flashlight shining it at a sharp angle against the screen do you see a giant image of your desktop background & icons? If you do you know what we’ll need to focus on here. Let us know what you see or don’t see ;-}