Be willing to negotiate
After working for two manufacturers, one with a large appliance presence, I learned a few things.
First: To find out truly what is wrong, most manufacturers are willing to give you a free EVALUATION (only) of the appliance by an authorized servicer to find out what is wrong. If an evaluation by an authorized servicer is already done, the manufacturer will take that info at face value. Hearsay will not work. A servicer must have visited the appliance and have the diagnosis on record.
Second: Most of the time the manufacturer will spot you the parts for free if you pay the labor if the warranty has expired fairly recently. This is a pretty good deal as a picture tube, compressor or LCD panel failure early in the life of the unit is pretty rare and the device will probably work for many years after repair.
Third: The manufacturer’s name is on the unit and the manufacturer’s reputation is at stake. I worked for two Japanese manufacturers. I have seen almost ridiculous extensions of warranties because “our name and reputation is on the unit”. In one case, a microwave oven, we did a ridiculous extension of warranty because, (as I remember) one Japanese manager put it, “ We designed the unit to last twenty years, the customer did not deserve this expensive of a repair this early. Fix it.”