What to Do If a Laptop Shuts Down Instantly with a Hard Drive Attached

I have a Dell Latitude E5570 and when I got it, all it was missing was a HDD drive cable (the cable in the bottom that connects the hard drive to the motherboard). The image shows the HDD cable unplugged from the system sitting beside it. I just added it for reference.

Well, I finally got my hands on that cable, but when it's plugged in, the computer won't boot whatsoever. The power light turns on for a brief moment on the power button and then proceeds to shuts off. No fans start, no response on the screen, just on and off quickly.

And yesterday, when I was trying to install Windows on an external drive to run it, the computer fired up fine when the HDD drive cable wasn't plugged in. But the moment that cable is plugged in, the computer just won't fire up even a little bit. I even had it unplugged, and then after the computer started to boo,t I plugged in the HDD drive cable and it shut the computer off.

The situation doesn't change when an HDD is plugged into the cable; it's just when I plug it in on the bottom. The laptop stops even trying to work.

I'm really, really scratching my head here and could use some help cause I've been computerless for a while and basically my life revolves around it.