the reason they fail while starting the car is because with the key in the "start" position very few things are actually getting power, the cig lighter is not getting power in that position.
once the car is started it should come back on though.
my inverter is a 350w normal, but 700 peak. it is just a cheapy I bought 3 years ago, but it still works great.
but if ours is a 400w peak (they tend to advertise the peak, to get you to buy it). then I doubt it has a high enough normal output to keep your laptop charger happy.
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1994 Honda civic CX hatchback (BIG MPG) STAYING STOCK
*******1999 GT SOLD*****