The sprint button on the Xbox controller is activated by pushing down on the left joystick. This is a mechanical switch that is depressed, and will usually make a click sound when activated. The button can have a mechanical failure, where the button is not being depressed, or an electrical failure, where the switch is not making contact. The fix described here is related to an electrical failure of the switch, but also briefly describes the mechanical action of the switch.
Torx-8 security screwdriver. This fix requires you to open the Xbox controller. This requires a Torx-8 (T8) security screwdriver. If a security screwdriver is not available, a regular T8 can be used, but the security pin inside each screw will need to be snapped off.
Continuity Tester. We need to check and see if the switch is conducting when depressed. You can use an ohm-meter for this.
Soldering iron and de-soldering tool. This fix requires removal of components from the circuit board of the Xbox controller. This requires a soldering iron and a de-solder pump, or de-solder braid. If you are not familiar with de-soldering equipment, it may be best to ask someone with experience to remove the components from the circuit board
Step 1: Open the Xbox controller
Remove the 7 screws from the bottom of the Xbox controller. 6 of these screws are visible, 1 is hidden under the battery pack, under the serial number sticker.
If you only have a T8 screwdriver, break off the security pin inside each screw. I do this with a hole punch tool. Pushing the tool into the screw head bends the center pin. Once the pin is bent, push the tool into the screw head beside the bent pin, and it snaps off.
Once the screws are removed, take off the plastic cover of the controller. Remove the circuit board. There are 2 vibration motors attached to the circuit board. Remove the connectors from the circuit board so that the motors are not attached to the circuit board.