Cadillac Grinding Noise When Accelerating

1998 Cadillac Deville grinds when accelerating. What causes this problem and how to correct the problem?
 Can you describe the noise a little more? Is it engine speed related, vehicle speed related, do you hear it under the hood or only inside the car?

The noise sounds like growling when accelerating from a stop position. The noise comes from the driver side. When the car accelerates from a stop position.
 OK. Then you may have a bad motor mount. This can cause the engine to vibrate on the frame and give the noise and a grinding feel.

I have been told that the traction control sensor is faulty. The message reads traction control engaged.
 OK. That helps. Then yes, you may have an ABS wheels speed sensor acting up. This tells the computer what the wheels speeds are. If it sees one different from the others, it activates and will give a noise.

So do I understand that ABS and traction control are the same?
 They work together. ABS stops wheels slip during braking, traction control prevents wheel spin during acceleration. The system has a lot of wiring and many sensors.

I also have been given a suggestion to replace the traction control harness. Does this mean it is an electrical problem? So, my question is,to correct the problem, do I replace the harness or a the left joint? The car was put on a diagnostic machine which indicated that the codes indicated a faulty traction control sensor.
 The system has a lot of wiring and many sensors. If the left front ABS sensor harness was diagnosed as being bad, then yes this should fix your problem. That, or the right front harness are common for breaking wires inside the insulation and the harness would need to be repaired or replaced. Not the whole traction / ABS harness, just the section to the left front wheel speed sensor.

I also had another automotive center check the problem by codes, and I was told that no codes were available to show the problem. I think I'm getting the run around
 It is possible that the codes were not still in the computer when it was at the other shop. Sometimes codes will be erased from the car computer memory after a pre-determined time has gone by that the computer did not detect a problem.

Now what do I do?
 I would go by what the shop that read codes said. It makes sense you are getting a traction warning, noise in left front, and they determined the left front sensor harness was bad.