Disclaimer: The following instructions are a compilation of what I learned after a few hours of research online, I am not an IT professional.
I hope these instructions will be useful to others who have run into similar problems with their faulty hard drives and allow them to recover their data.
Step 1: Diagnose Your Drive
Mechanical failure can manifest itself in many different forms, the most common of which is an abnormally loud repetitive clicking sound.
When there is an electrical failure the drive will generally not respond at all to being powered on, you will not hear the platters spin up.
In my case when I powered up my drive I could not hear the platters spin up and heard no other noise coming from the drive. I also touched each of the integrated circuits (ICs) on the controller and found that one of the them was very hot (refer to picture). The hot IC was a clear indicator for me that the controller was the problem, although even if you don't have an over heating IC the controller could still be the problem.
Step 2: Find the Serial / Part Numbers on the Drive
Drive Code Number: YAR41BW0
First 7-digits of the drive Model Number: 6Y080L0
9-Digit Code number on the largest IC on the controller: 040111500
Edit: Also I found that not all models of Maxtor hard drives have bios chips (refer to picture). If your old controller has one then make sure your new controller does as well. If your old controller does not have a bios chip then I assume you will want to find one that also does not have a bios chip.
Step 3: Procure a New Controller
1. Go to ebay and find a working drive for sale that matches all of your numbers, buy it and cannibalize the controller. I investigated this option first but was unable to find a match for my drive, you may have better luck.
2. Find a supplier that sells new replacement controller, they will be more expensive than option number one, but you will be paying for a new part and will morel likely find the exact controller you are looking for. This is the option that I went with.
This is the vendor I used:
Hard Drive Parts.com
Step 4: Procure an Interface to Your PC or Laptop
Step 5: Replacing the Controller
1. Ground yourself before you start handling the boards.
2. Remove all the fasteners holding down the controller board. (Mine had 5)
3. Gently pull out the controller board
4. Carefully, without tearing, remove the foam from the bottom of the old controller board.
5. Place the foam in position on the hard drive making sure not to obstruct the two groups of electrical contacts.
6. Place the new controller on the hard drive
7. Replace the fasteners and tighten snugly.
Step 6: Download Your Data
I am not sure if the order matters, but I first connected the USB to IDE adapter between my Laptop and hard drive, then I powered up the hard drive.
I used a PC power supply to run power the drive while I backed up the data. If you use this method you will need to take a paper clip and short the green wire to the black wire in the 24 pin connector to get the power supply to turn on.
If you are fortunate enough to get your hard drive to come back to life, don't dilly dally, back up all your data ASAP, just in case something else decides to fail.