Nick & List,
These cheap 12V input inverters often have a high idle current. Some draw 150mA or more, on no load.
The immobiliser in my wife's Peugeot 106 diesel, also has a heavy draw on the battery, if left in the "drive" condition. It also will flatten a good battery in a few hours (especially in cod weather) - effectively immobilising the car.
There are many of the 12V inverters available, some even claiming 5kW continuous and 10kW peak power. Clearly drawing 5kW plus froma car battery is impractical from the large currents involved, which would need very heavy duty cables.
IMHO, anything more than a 3kW inverter should have an input voltage of at least 48V, in order to keep the input current manageable. Drawing several hundred amps from any sensible sized 12V battery is a sure fire way to an early battery demise.
My 5kW continuous rated inverter has a 108V dc input, but then it was UK designed and built in the early 1990s, before the advent of cost-cutting cheap chinese junk.
At the end of the day, you get what you pay for. A well engineered, continuously rated 3kW inverter designed specifically for solar or wind power off-grid applications (such as SMC WindyBoy) will cost about =A33000, and not the $599.99 as seen on a well known online auction site.
Ken