I just bought a 200 watt rms/ 400 watt peak power inverter to power only my xbox. i have a cigarette lighter hidden under some console and have a spilt in that to allow two divices to be connected. my lcd is in the one so i connected the inverter and xbox to the other. with this configuration the xbox would only power on for a split second. I know that the invertor has high enough wattage cuz it worked in my other car. I believe that by hardwiring the inverter to the battery with a 4 guage wire and inline 80 amp fuse, i should be ok. The invertor i purchasedonly has a cigarette lighter kit, no hardwire kit, but i plan to modify it. Which is the positive and negative in the lighter? is the tip the negative and the sides the positve or is it the other way around. Are there problems with me doing it in this way? thanks!
Use your meter to verify, but typically the tip is positive and the side is negative.
Something to consider is that, in RV applications, the inverter is mounted with as short as possible DC leads, and the AC side is where the long runs of wire takes place..
400 watts in DC is approx 35 amps while in AC it's less than 4 amps.
Regards,
Jim
Don't how this help or not but I think your power wire is way too big. The inverter might shutdown early if your battery is low because of the big wire.

You could just run your own wires for the inverter and not use the cig lighter at all.