I created a very simple 1-wire software to detect the presence of the EEPROM. And looking at my oscilloscope.
The TF2929 doesn't respond. Explanation: On the datasheet of the EEPROM, it says there that after a Reset Low Time (in this case, it is 488microseconds), the EEPROM should respond 15 to 60microseconds after the rising edge of the Reset Low Time. As seen here, there is no reply from the TF2929 and I am confident that it is dead. Frustratingly, I can't do much at this point. Even if I buy a new TF2929, I don't have the binary file to be written to the EEPROM.
I even checked the laptop and I can see that it is sending pulses but the TF2929 doesn't respond as well. (Sorry, no screenshots) Therefore, the laptop's 1-wire master is working fine and I don't need to do anything on the mainboard.
The question now is why it happened. This is how it was implemented.
Open-drain circuits can fail and one of their symptoms is that they couldn't sink any current and I had seen this happen. It is possible that the TF2929 can receive messages but it can't respond back because their open-drain output has been damage. If I'm the engineer in charge for this circuit, I will make it like this:
Wherein R is around 50ohms and/or not lower than 22 ohms.
Now, the only feasible thing to do at this point is to buy a replacement 90W AC adapter.
Update: Sept 25, 2016
I bought a second hand Dell 90W AC Adapter for 7 US dollar. All my findings above are correct. Now my laptop can recognize the 90W Adapter and is now running again on full speed.