How do I replace or fix this electronic chip?
That doesn't look like a burned resistor to me. Looks more like residue from a poorly cleaned board. Generally speaking, a fried resistor is a symptom of something else failing and not the root cause (although again, I suspect this is not what happened here). You could try reflowing it (get some soldering flux and a reflow iron or soldering iron and clean up that area) or at minimum using isopropyl alcohol + toothbrush to scrub that area and rinse it with water to clean the residue off and verify that the resistor is soldered properly.

Another quick+easy debugging step is to use the thumb test. Power it on and check for hotspots on the board; if one (or more) of the components on that board heats up considerably, it's fried and you'll need to replace them. You shouldn't do this with a battery, but with a current limited power supply (with a fairly low current setting, to avoid risking damage to the PCB).