If the fan is racing it’s safe to say the power supply is working as the SMC logic is doing what it should be trying to keep the system cool as the thermal sensors in the display have been disconnected so the system goes into Safe Mode.
Did you get a new display yet? Your system will need it to work properly.
So looking at the onboard diagnostic LED’s which you are still having problems
LED 2 - Indicates that computer is turned on. This LED will be ON as long as computer is turned on (but is not asleep) and power supply and voltage regulators are working correctly. I think given the fact SMC is working (fan racing) the onboard VRM’s have an issue powering the CPU. As you replaced the thermal paste I’m suspecting the CPU chip is not properly seated or the one or more of the socket pins are bent. Did you replace the chip with another? Then its the wrong CPU.
LED 3 - Indicates that computer and graphic process unit (GPU) are communicating. This LED will be ON when computer is communicating properly with the GPU. If LEDs 1 and 2 are ON and you heard the startup sound, but LED 3 is OFF, then the backup battery (on back of logic board) may need to be reseated, or the logic board may require replacement. This won’t happen until LED #2 has passed
LED 4 - Indicates that computer and LCD panel are communicating. This LED will be ON when computer is turned on and video signal is being generated. If LED 4 is ON and there is no image on display, then the LCD panel or the cables between LCD and logic board might be installed incorrectly, or need replacement. This won’t happen until LED 2 & 3 have passed and you have reconnected the LCD to your system via the extension cables or directly.