I have a mid-2013 Air (i5, 4 GB ram, 120 ssd, El Capitan) that has started to experience sudden shut down and power issues. For the past few hours, I can power up the Air, log in, and the Air will just suddenly power off regardless of battery level and whether it is or is not connected to a charger. No liquid damage, fan spins when it powers on, healthy battery, trackpad, keyboard, USB ports, and charging port work. After suddenly powering off, it will not power on using the power button unless I leave it in its powered-off state for a few minutes. A couple of times, after pressing the power button, the Air would power on about 1 to 2 minutes after I pressed the power button. What I have tried so far: using an 85, 60, and 45 watt charger; reset smc and nvram; tried running internet recovery, booting from an El Capitan USB install key, and an external drive running a clean install of El Capitan but none of this works as the machine will suddenly power off after being on a few minutes; and trying with and without the battery connected. Apple Store says the logic board needs to be replaced at great cost. I have heard that a replacement trackpad IPD cable may be the solution. Anyone who is able to provide information on this issue would be greatly appreciated. Thank you.