Well, I would a continuity test. You take the leads of an multimeter and check for continuity of a circuit, usually the resistor in suspect. if you dont want to do that, you'll need to check each sub circuit assembly via a shematic diagram and see if its volatge out or current source matches its schematic reresentation. if not, something loopy is wrong with the circuit.
but of course, you probably dont want that. do a continuity test.
If said resistor is truely 'burnt' then it should be obvious where it is, as it'll look different. Black, possibly with some black stuff around it on the PCB, and its colour code (value code if its SMT) would probably be worn off.
Then again, as you're looking for a 'burnt' one, I assume its a higher wattage resistor? like 5W wirewound or something, in which case you can't always tell, and you'll have to do the suggested continuity test.
The component burnt without identity and no comparable equipment where from the value could be read out, and no schematic, either? Nice situation. we may have to reverse engineer the part of the circuit where the burnt resistor is a part. then depending on the case, we may have to evaluate its value. this evaluation would always be approximate and then we have to substitute and try. It calls for some design capability and elementary electrical and electronic application (includes solid state or vacuum tube, as the case may be) capability.
As has been sought by seniors already, try to provide a clear case study and with clear and focused close-up shots, duly compressed and sized to fit to avoid bandwidth wastage. this help us to help you in return.