A link to the inverters you ordered might help to understand the problem.
Doesn't your laptop have a battery? That's the common way to work with it in a car, plane or public transport.
I am trying to power my Lenovo G510 while at work in a vehicle, and I'm having a devil of a time finding the proper inverter to do this. I have already ordered and tried 4 different inverters from Amazon, and not one works. I have tried anywhere from a 200W up to 500W inverters. My laptop is 65W, and the AC adapter says:
INPUT: 100-240v,1.8a, 50-60Hz
OUTPUT: 20v, 3.25a.