If you happen to have a spare mouse on hand. What you can do to make sure that the mouse is putting out a signal to your iMac is: 1. Turn off the mouse. 2. With the additional mouse if you have one, go to Apple Logo in the top right corner then System Preferences -> Bluetooth. 3. From here, make sure the mouse has good, charged, batteries in it. 4. Power on the mouse. 5. You should be able to view the mouse at this point. Select the Mouse you would wish to connect and you should be able to view your cursor again. If you only have a keyboard working. You may be able to use the spotlight command by clicking the "Space Bar" + "Command Key" at the same time. type in Bluetooth and hit enter. It should pull up the Bluetooth menu and you will have to attempt to navigate it with the Arrow Keys on your keyboard. If you are still having issues with the mouse, it maybe time for a new one. Let me know if this helped!
It may not be something that needs a repair! A lot of people run in to this same issue and most of the time it can be fixed by a specific order of powering the devices. First off go ahead and power down the Macbook pro. Now make sure that the cinema display is plugged into the Macbook pro, all three cables. USB, Mini display, and a power cable. Now boot the Macbook Pro, and if all is okay with the monitor it should power on at this point with the Macbook pro. Let me know if this helped!
From what you have described it sounds like a temperature sensor is either having issues with: 1. Reading the right temperature. 2. Has been knocked out of place or tampered with. 3. Your Monitor is actually heating up to a temperature in which the computer believes it should turn that fan on high. If you really think that it is an issue with the temperature sensor, and not your computer actually over heating. I recommend the program Macs Fan Control (http://www.crystalidea.com/macs-fan-control). This program will allow you to adjust the RPM of your fans and also view in Celsius or Fahrenheit what temperature the components in your computer are at.
When it comes to Apple a blue screen is never a good sign. Normally relating to either Logic board damage or Water damage. There are some ways to trouble shoot the device though! If the blue screen is occurring continuously you may want to attempt a restore on the device. As long as the data is not a factor or if you have an iCloud back up for the device I recommend the restore. After the restore, if you are still experiencing the blue screen there may be damage to the board. To prevent this issue from happening remember to: 1. Always be grounded when touching on or near the logic board of you device. 2. Keep your screws in order and place them back in the exact spot you removed them from. 3. Don't over tighten your screws. Ever. The digitizer being unresponsive can be couple of things: 1. A defective part is a possibility, if you have another screen on hand give it a try. 2. I know you have already taken it out and placed it back in but make sure it is connected properly. 3. Finally, if it is related to...