The resistor almost certainly burnt because one of the electrolytic capacitors (ecaps) shorted to ground through the resistor. The ecaps are the cylinders with aluminum tops and an X on top. These are
the most common failure on old equipment. They can go short or they can blow up or they can bulge before they blow up.
They are polar, and if you wire them backwards they will pop. BTDT.
I have a page about ecaps if you are interested -
https://www.nmr.mgh.harvard.edu/~reese/ ... index.html
This is targeted at old vacuum tube equipment that run high voltages, but much of the discussion is relevant to ecaps in general, including the low voltage types in this board.
The resistor pointed out above is a SMD (surface mount device). Not easy to replace unless you have experience with them. You could replace with an axial resistor as reasonably suggested above, by soldering across where the trace goes. If the traces are not damaged, you could instead solder in a new SMD resistor in the same place. Either type of resistor is easy to get. All well covered above.
If you want to replace a SMD, there are You Tube videos that show you how. Clean the circuit board pads and tin them, apply a little liquid flux, hold the device on the pads with tweezers, and touch the tip of the iron to one side of the device. It will be stuck and you can solder the other side with a little more solder wire, then go back to the first side and finish up with a touch more solder. Easy if your vision is good and your hands don't shake.
Two issues that have not been mentioned -
I expect that burnt resistor won't have any readable markings now. You could guess that it's the same as the other two resistors that are nearby, and get in there with a magnifying glass to read them. Or someone with an undamaged board could read the value on the resistor (above poster?)
I would replace all the electrolytic capacitors on that board (five of them). If one is done, they are all done (looking back this has been mentioned). Easy and cheap if you can solder at all. Look on YouTube for videos about desoldering.
Possible there is something else wrong with it. Probably not. You have to fix these issues before you can test it any further.