the voltage regulator is probably out and thats why that resistor is
burned, if you change it, you will just roast another one. look for the
nearest chip attached to a heat sink , flip the pcb and look at the
traceings, are they browned? check the diodes nearby also, voltage
regulator chip (trnasistor type = around $5 or so, ic type up to like $30)
from my experience just about all tv sets with power supply failures like
that (burned components, or no power) are due to a bad vr chip, it
produces a lot of heat and wears out due to it, if you change it make sure
that you attach it back to the heat sink with the heat transfer grease or
patch in place if it has one. you will need to replace the resistor as
well and any other component damaged due to excessive current