As you have done all that the LG rep said, phone faulty. They know their phones.
Have you thought about going to the shop of the network you are on? most have a high street shop, It is in their interest, for you to have your phone working. A lot, will give you a loan phone for holiday, might not be the same phone, At least you will have a phone.
Haggle a bit, you never know.
SD, October 2011