Hello and welcome to Android Forums. Hopefully I can help you with your problem.
Well, you have several choices.
1) Is the phone still under factory warranty? Factory warranty is usually 1 year. If it is, contact LG and tell them you need to send a device in for service and explain that it's not powering on. They'll ask you for the phone info. All you need can be located in the battery compartment. If you are unsure if the phone is still under warranty, give LG the MEID or ESN and they can tell you whether or not it's still covered.
2) ( if not still under warranty ) Do you have a local repair store? See how much they will charge you to fix the phone IF and I do say IF it can be fixed. Depending on what's wrong, there is a good chance you'll come out cheaper just getting a new phone.
If you have any other questions regarding your device, I invite you to join Android Forums. We have many sections for specific devices which contain a wealth of information.