you might've fixed the problem by reseating that power connector. However if the problem comes back, you could have a failing power supply. They do age over time. How old is that computer?
I've got a Lenovo 3000 H210 that will not boot. When I press the power button, the light comes on and the fan starts up for a few seconds and then stops and the power light turns off. The fan comes back on for a few seconds, and then off again. I checked all of the connections inside the tower. All were secure. So I started to disconnect cables and try to boot. After disconnecting the P2 cable (labeled as 12v power connector), the power stayed on. What do I need to replace??