This depends on your contract. You say that the salesman told you they would REPLACE if they could not REPAIR. This means that they are required to replace the unit. They do not have to replace it with a new model, but they must replace it with a comparable one.
If they are failing to replace it, or offering to give you only a fraction of the cost of replacement, then yes, you would be entitled to the difference in court.
The only downside is the cost of litigation
(how much is your time worth plus the incidentals of litigation, filing fees, service, copying, etc.), and the inherent risk of a lawsuit (there is always a chance you might lose, no matter how strong your case is). So once you balance that out, you can make an educated decision as to whether or not you want to pursue an action to force them to acknowledge their duties and obligations.
There may be another route - you can try for mediation through an entity such as the Better Business Bureau
(it is voluntary so LG may not participate), but it is a much cheaper option.