[COLOR="Blue"]First the problem is vegetables/fruits are freezing, milk turns into some what like slurpy and water drips out of the ice maker drawer.[/COLOR]
Sounds like a problem with the damper control system which regulates the amount of cold air entering the fresh food section.

[COLOR="Blue"]I bought a side by side refrigerator from Home Depot about 3 years ago along with a 5 years extended warranty. It had few problems and GE was able to send someone who knew what to look for an repaired it. Now It has a problem that this person does not seem to konw how to fix it and GE informed me at their public relation that this the best they can do for me in the whole state of California.This person has been trying to fix it since Dec. 15, 2009.[/COLOR]
I would pull out the warranty and the extended warranty documents and carefully read the terms and conditions.
In my opinion GE does have other options re: replace the unit with a comparable unit or refund your purchase price.
Sit down and document the service history of this unit, including any problems you have had with service re: canceled calls or showing up late etc.
Do not try to fix it yourself as this could give them an excuse to cancel your warranty.
They have an obligation to fix it, if this person cannot then in my opinion they should get someone in who can.
If they have to fly someone from where ever is not your concern.
They contracted to keep this thing running and it is not.
Also what it costs them to fix it is not your concern.
When contacting them be polite but firm and always document the calls and be sure to get the person's name.
If they do offer you a settlement I would not settle for anything less than full purchase price. After all you purchased full warranty extension.

The above is just my opinion and hopefully others will jump in with suggestions for you.