which one is the right pin, there isn o pin, there is a cpu_fan connetor, whic has 4 pins, the cpu fan must go there
if the system doesn't detect the cpu fan it will not work
if the fan is not working properly, or system can't detect it, remove that fan an replace it, if you need a new an and heatsink, try that
the cpu will not melt, could end burned bt that only happens under the metallic shield the cpu has, so you can't see the damage caused and if it shut down, very unlikely it never reached that state
now, you move a cable, what cable, do cable management with a pc turned on is a danger for both the person and the pc, you can do easily a electorstatic discharge over any component and that does kill mainboards
if you can, take pictures of the pc, the area of the cpu and give details of the hardware you have there
while at it, with the pc turned off and disconnected, remove the battery and the ram sticks, reseat ram and the battery, connect pc again and turn it on to see if any of the previous recommendations helped and please, turn off your pc when managing parts and cables