If a resistor is burning up, either:
(1) it has increased in value and is dropping excessive voltage;
(2) the source voltage at the high side of the resistor has increased;
(3) the load on the downside of the resistor is shorted or nearly shorted.
The most common cause is (3). Using a DMM, measure the voltage on both sides of the resistor. The one with the higher voltage is the high side; the lower voltage indicates the low side. Is this positive or negative? If it is positive, turn the machine off. Using a cliplead and a 100 ohm resistor, discharge the residual voltage on the low side of the resistor, and then measure the resistance between that point and ground. Make sure the positive lead of the ohmmeter is on the measurement point and the negative lead hooked to ground. If the voltage is negative, follow the same procedure, except hook the positive lead to ground and touch the negative probe on the meter to the measurement point.
This will turn up a short or near short.
Don't be surprised if the problem is due to a bad capacitor. Caps located next to power resistors have a VERY high failure rate. Often these are 85-degree caps; most techs these days replace them with 105-degree caps.
Sometimes a cap that is beginning to short will run very hot. You can often find this with the "finger" probe.
Best,
Fred Longworth