I have a portable 300 watt inverter in my RV that I will plug into the cigarette lighter, and run things like the TV or laptop.
My buddy has a 500 watt inverter from Costco - $40. Same thing. We both have a dedicated #10 wire to the cigarette lighter, with a 20 amp fuse, so they are good for about a 200 watt load.
I used to run a Dirt Devil from the 300 watt inverter - when it was plugged into a #10 wired cigarette lighter and 30 amp fuse. It can be done.
Sorry to hear that your inverter is toast. Have you tried plugging it in someplace else, or directly to the battery?
Good luck,
Fred.