I'm trying to measure this resistor using an analog multimeter which has resistor parameters from X1 to X10k, but whatever parameters I set to, the needle doesn't move.
The resistor unusually has a white final band.
The final white band normally means a fusible resistor (though there are many other colour combinations as detailed in Colour codes for fusible or non-flammable resistors).
Fusible resistors combine the function of a fuse with that of a current limiting resistor. They are designed to fail open (like a fuse) under overload conditions, and are commonly used as protection devices in power supplies.
When they fail, sometimes you see clear burn marks, other times they just fail open circuit (which would fit with your case).
To maintain device safety, they must only be replaced with new fusible resistors not just plain resistors.
You also almost always have to identify and fix the underlying cause of overload, as otherwise any new fusible resistor will just fail straight away.
In this specific case, gold would be 5% tolerance, and the two orange bands give 33. That just leaves the middle multiplier band.
From the photo it looks green, but I wonder if this is an artefact and it is actually black? In that case the multiplier is 1.
My guess would therefore be a 33R 5% fusible resistor, but you need to confirm if the middle band is black or green. To determine wattage you'd need to compare physical size with other similar fusible resistors.