I would think this is a BIOS or motherboard design fault.
basically what happens, when you plug it in, there's some circuits that begin functioning like battery charger, some LEDs etc.
it's similar like if you take a WD external HDD and just plug it in, it will power on for a few seconds then detect that there's no data connection and shut off. I don't know, maybe they've solved that issue by now, not that it's a big problem.
So, in case with a laptop, I'd think it's a similar issue, it detects AC power, essentially the motherboard turns on at that point. So maybe in your case the motherboard is faulty or BIOS is not configured properly and it does a false start.
here's a few options to check out:
- update BIOS if possible
- do the laptops have functioning battery?
- how about CMOS/BIOS battery?
basically, pull out the laptop battery let the laptop sit for a bit then plug in, do you get the same behavior? also, unplug the battery, unplug ac, hold the power on button for 10 seconds, then plug in DC and check what happens. Does the BIOS time reset? Does it reset when you just take out the laptop battery?
Basically there's 3 power sources for the motherboard ac adapter, laptop battery and CMOS battery (I think newer laptops are beginning to omit this one). If either of them goes bad or is malfunctioning you might experience strange behavior.
Also, if you have a possibility try a different charger and different battery (if you have same in household or borrow somewhere)
So experiment a little bit, let us know what you find.
In the end it might be just a motherboard hardware fault in relation to power adapter that there's nothing you can do about it.