Just to post an update and close this thread I will explain how I found what’s wrong with the motherboard…
The problem was with the bad solder on Zener diode D7012, and I found this by measuring the voltage on the capacitor C7012 - on pad 1 of the capacitor I was getting around 15V (voltage from the MagSafe) but on the pad 2 of the capacitor I was getting around 14V which is not good. The voltage on pad 2 of C7012 needs to be around 6.8V because of the Zener diode (GDZT2R6.8) that pulls down the voltage. This voltage drop is needed in order for Q7010 to open and send the same voltage on pin 1 (6.8V). Since I was not getting the right voltages I checked the diode under the microscope and found that one pad was not soldered correctly.
I also replaced the diode with another one, but since I didn’t have the MacBook donor board I used the diode from the iPhone 5S motherboard :) It is the same diode but the one from the iPhone board is rated at 6.2V instead of 6.8V, but anyway it works :) This diode is placed near the LCD connector on the iPhone board.
I hope this will help someone else to solve the problem.