Interesting puzzle. So far the most useful guesses to me are those made by
@dlgoff in comment
#2 and
@jim hardy in
#6. Clearly this is a smallish power resistor compared to all those SMC's on the board. I too searched for a schematic and/or service manual (yes, I have a
lot of time on my hands some mornings) and like the OP I came up empty.
As Jim points out, that sort of diode is often associated with a power supply. A DC battery wouldn't require rectification, but what about a generator working off the wheels (wild guess)? If the OP (
@carlos468) were
extremely obsessive-compulsive and had no other real-world responsibilities to attend to (e.g. no job, wife, or child), he could sketch a partial layout (and from that a schematic) for that part of the board, getting values for other nearby components by inspecting them; hopefully the board is no more than double-sided, which means you'd still have to look for via's (little holes which connect traces on the opposing sides) and also identify the ground plane. You wouldn't have to do the entire board, just enough that someone could take a good guess at this part of the circuit. I once drew both sides of a PCB for a guitar amplifier, just so I could analyze the layout; so it can be done.
However - one thing that gives me pause is, the fact that the resistor burned out in the first place - as the OP says, apparently when the previous owner somehow plugged a charger in (no details given by the OP on what this entailed). Sometimes a resistor will literally "take the heat" and protect the rest of a circuit by burning open, almost like a fuse; but often even when that is the design intent, it isn't always enough. Thus the possibility exists that even as the resistor was toasting, more sensitive components such as ICs and transistors were getting killed; typically this happens without leaving visible evidence. Possible support for this theory is that if the resistor still measures as having resistance, rather than being open-circuit, that means it didn't get sufficiently fried to stop conducting or even to alter its value as hugely as it might have; which in turn may mean that it's not be to blame for the circuit not working. I am guessing there are at least transistors on that board, as I see a lot of three-legged creatures in the photo that seem to have "Q" associated with their part label; but that's just a guess as my solid-state knowledge is pretty limited.
At any rate I would be wary of committing a huge amount of time to worrying about exactly what resistor it was, without a better sense of what the previous owner did as well as a plan for identifying and checking the status of the semiconductors on the board. Without a schematic and some experience at checking voltages for transistors & ICs and so forth it would be very difficult to tell. You could just get yourself a half-watt 10K resistor and a new diode and solder them in place & see what happens. If no joy, then the most efficient option might be to find a service shop that could at least take a quick look (good service shops will do that). Some product companies will supply replacement boards to repair shops; others won't. But this little board looks simple enough that potentially a capable repair shop could replace bad parts and get it running again.
