I had a similar issue. When you pull the trigger the light came on but the chuck would not turn. No sound or smell, the chuck just didn't engage. When I took it apart I found there was a cold solder joint on the red lead to the motor which came loose.
The thermal switch I used as a replacement was a Klixon 7AM 026 Thermal Protector - 95 C - 203 F - N.C. - 7AM026A5. I purchased from MOPS Electric via ebay in case anyone has the same issue.
For my drill, the Torx screw had to be rotated *counter-clockwise to remove. I'm not sure if that was an error in step #5 or some drills are different.