Hardrive or hardrive cables?

I took my iMac into the Apple Store because of the dreaded flashing file with question mark. At the Apple Store they ran diagnostic. I was told it could be the hard drive or the cables to the hard drive could be loose or need replacing.

I used fixit guides to open up my iMac (thanks for great instructions and videos) I cleaned my fans got all dust out with a soft toothbrush, however I found the hard drive cables were connected properly.

Now my dilemma, before I replace the hard drive is there a way to test it to see if it's really dead? Is it cheaper to replace cables, should I do that first? Is there a device that can tell you while you have the hard drive out if it's bad. Or, is there a way to connect it to another Mac to see if its' good?

I have a newer Mac mini with an i5 quad core. Just want to know and also need recover any data from that old HD if possible.

Thank you.