When you started the computer was the car running? If so then it would be running off the alt until the battery became charged.
When i first installed it and turned off the computer but left the inverter on and plugged into the lighter, my battery was dead (needed a jump the next morning). The battery was old so I went and got a new one. Even now with a new battery if I turn off the computer but leave the inverter on, plugged in, the engine turns over slower the next morning. I'm sure the inverter is drawing enough to drain the battery even when it's not being used. The inverter is suppose to have a low battery shutoff but I don't think it's set high enough.