I'm running a laptop in my SUV... but I don't use an inverter... I use the car/airplane
adapter for my laptop... it does the dc-dc conversion for you and charges and powers
Mine is on as soon as you have ignition to power the laptop. I still have the battery
in the laptop for a backup and to let the laptop stay on during cranking or short trips
in and out of the car.
I'm sure you can find the auto adapter for you laptop pretty cheap on ebay.. $30ish...
Here is the brand I have... very popular and works well.. Lind Electronics