Shut off all power to it all, Pull off the cable properly, check all the pin points of the connector. , first see if any have slid back in the plastic.
If they are all settled proper and at the same distance in the connection. Check also for charring of the wiring, or connection areas, melting of the plastic.
Next check the motherboard itself if any of the connection points in that connection are not straight.
next you can slide the connector on and off a few times and any oxidation of the metals will roll off, making more raw clean metal connection places. Oxidation is an insulator not a conductor, by sliding it in and out a few times the area of connection will have some oxidation rolled off. Older stock PSUs and motherboards it would be common for the connections to have a build up of oxidised metals on it. I make it a regular practice to carefully slide these on and off 2 times (OCD style) when building a unit, before fully slotting it in.
It could be the "crimp" used to put the connectors onto the ends of the wires is the problem, at times I have even soldered those on fully, but recrimping could also work. Bad crimps can be seen when it is inside the plastic some, they will really stand out if you dissassemble the connector by removing all the wires+connection out of the plastic.
Bending the connections , yea it is possible, but it might not be very long term, vrses replacing it with something better. Bad connections like that can generate heat there, which can even melt the connection.
Bad power connections going to Mosfet switching stuff can cause fet switching to not be complete (reduced voltage due to not enough amps for the load) When that happens it can completly damage these switching components, If it is not fixed fully, you should know there is the possibility of damaging stuff that is even more expencive. . . Also you shouldnt really be pulling on cords like that to make things happen :-) because it just adds to the issues.
What is the light item that blinks on that board specific to? lights like that can be ram, sata controller, and other status lights, that may very well have the function of blinking when there is data flow (hd light).
It could also be that the connector on the motherboard has a poor solder joint, there can be much patch soldering going that is manually done after a motherboard leaves the machines, you could have 1or2 bad joints there, which you might be able to visually see. Because they are fat power connection places, an average tech with a great hot soldering pencil (copper core type) could patch anything there.