Asus Zenbook UX31A not booting

I have been trying to repair a Asus Zenbook UX31A for quite some time and would like to pick your brains, because I am finally out of ideas.

When I received the Zenbook it was not booting, not reacting at all (no lights whatsoever). I then started using my multimeter to analyse if the AC adapter, the battery or any other component was faulty. However, it seemed the device was getting the necessary voltage/amps (i.e. 19V and 2.37A), although the battery seemed to be rather low. However, I would have expected some kind of reaction.

After some additional research I found that this device often has issues because of the power button being part of the keyboard rather than a separate button. Similarly, people reported that Asus service had replaced their motherboards when they had similar problems.

I then went on to order a replacement battery, keyboard and motherboard. Neither battery nor keyboard seemed to change anything, which left me with the motherboard. And, not surprisingly, the laptop booted correctly after having replaced it. I realised that both batteries were quite low and charged them to about 40-50%. Later that evening, I plugged in the AC adapter again without booting the device.

A few hours later I attempted to boot the laptop again, but the lights only turned on for a few seconds, after which they turned off again and nothing happenend. I wasn't sure what the problem was, but suspected that it could only be related to the AC adapter, because the most important components had been changed. After that the laptop didn't boot anymore. Measuring the power supply revealed that their were no surges or anything alike.

I am now out of ideas and would appreciate if you could let me know your thoughts, as I would really like to get this device running again (it's only ~3 years old). Thanks in advance for your help!