did you read your warranty in the manual?
have to ask cause i know up here in the great white north LG have 2 years warranty not the standard one year
now as long as you promiss not to say brnt told you, some LG ranges had a defect that caused the control panel to discolor after self-clean, if yours is discolored, call into LG customer service and say you have read there was a problem with the discoloring, see if they will offer a new control panel for free, cause usually your servicer will come out with the whole head for the range(new touchpad,clock etc)
this should fix whatever the other problem is
and i know if i had to change that head i wouldn't be testing the oven before i changed the head and the oven vent
now in saying this....... if you do get it changed under warranty and after the service person is done the oven still doesn't work
BE HONEST and tell the servicer it never worked before they started!!!!! or they will be rechecking their work instead of looking elsewhere