Burning up resistor = too much current flowing through the resistor. From looking at the schematic, it seems that this can only be due to the series resistance to ground being really small (or nonexistent), or IC3 sourcing too much current for some reason. I would remove IC3 (if it's convenient), and measure the resistance to ground from the junction of R62 and R63. With the IC out, it should read about 60k. If it's a dead short, there's your problem, and you should look for solder bridges. Other than that, I don't know if electrolytic caps or op-amps can fail in such a way as to produce a short, but if so, C26 and IC3 would seem to be your best candidates.