The missing heat sink your ...

photo shows is not the processor, it is the North Bridge controller and it probably overheated.

Your processor is the one covered by that large and very dirty fan and heat sink.

You might be able to get a replacement heat sink for the controller although it looks like the attachment points are missing too (you might find a "stick on" replacement).

Until it is fixed you will continue to get the messwage you showed us or worse, you will get nothing on the screen at all once the controller is fataly fried.