I suspect that the repair costs for either(110VAC or 12VDC) will be about the same. In fact unless the TV cost more than $200 it would likely be cheaper to toss it and buy another one.
On a slightly different subject regarding 120VAC and 12VDC appliances. Many people have noticed that some of the 120VAC appliances use a 12VDC power supply. They then reason that they can just hook the appliance up to their 12VDC RV system.
I would strongly caution against this. Unless the appliance specifically comes with a cigarette ligher adaptor or states in the documentation that it can be wired to a automobile 12VDC system, DO NOT DO IT.
Why? The power from a cigarette lighter can vary from 10 to 14 volts, at least. The power coming from the power supply that came with the appliance is 12VDC, but it is regulated and is unlikely to vary more than 1 volt, if that. The wild swings and noise on the automotive 12VDC may be more than the appliance can stand.
The rule of thumb I use is:
a) If it comes with cigarette lighter adaptor, its ok.
b) If the documentation states that automotive power is ok, or the range of acceptable input power is 10-18 volts DC.
c) Otherwise, use the 120VAC power supply through an inverter. OR, buy a DC to DC Converter. They are not much more expensive than an inverter, $38 for a 50 watt unit (4.2 amps 12VDC). An example can be found at
Computronics and it can handle between 9.2-18 VDC.