How long will a 100 amp hour battery with an inverter run a 42 inch lcd tv?

100AH * 12v = 1200 Watts of power.

A 16 inch TV has a power rating of 55w, so 1200/55 is 21.8 hrs

Your TV will have a higher wattage (usually on a sticker on the back) so sub in the the value...

I would also minus off about 10% as the inverter uses power itself, and bear in mind this maths is for an ideal world, ie, fully charged, brand new battery, no other sources of drain (lights, DVD players), average volume/brightness etc...