Two things to think about. Firstly when something blows like this it might have done damage that you can't see to other components. So you might replace the resistor and it still doesn't work.
Secondly think about the component in context. It could be a super critical 1% resistor with a tiny temperature coefficient that controls something excatly. Or it might just be ballast, there to load down another part of the circuit enough so it works.
Consider the difference between:
- a resistor that controls an LED, replace it with something similar and it will be slightly brighter or dimmer
- a resistor as part of a critical tuning circuit, replace it exactly or it wont work!
So with that in mind, can you sketch out a little bit of the circuit? What does the resistor connect to? Imagining the circuit as a series of functional blocks, what do you think that block is?