Why is my hard drive not being recognized after replacing the cable?

I am getting a flashing folder with a question mark in it... This is even after replacing the HDD cable twice for this machine, with supposedly new parts. It boots fine off an external drive, and I have now replaced the cable twice and neither time have I gotten any love. Additionally, I should mention that I don't feel the drive spinning up when I connect the new cables (or old cable). I know the internal drive is good, because it boots other machines with no issues. Any ideas other than try a third cable?

Thanks!