A fan wire overheated and caught fire, and there is a scorch mark near the motherboard connection. I shut off the power supply before the damage got worse.
Can I remove the fan and use another header, or could the motherboard or CPU be damaged? What should I check before turning it on again?
Don't turn it back on just because other fan headers are available. A scorch mark means there may be damage beyond the connector, and it's not possible to tell from that alone whether the board is safe or the CPU is unaffected.
Unplug the power supply, leave it disconnected, and take clear photos of the header, the burned wire and the surrounding board. Contact the motherboard and fan manufacturers about inspection or a warranty claim. Keep the damaged parts rather than throwing them away.
Check exactly what was plugged in and where, once everything is unplugged. The motherboard manual should identify the header and its pinout. The fan model and a clear picture of the plug could help narrow down whether the connection was correct or a cable was damaged.
A fault in the fan or wiring is possible, but the scorch mark by itself doesn't establish the cause. Don't reuse the burned fan or cable.
Was there a splitter or fan hub on that header? Several fans powered from one header can exceed its current rating. Compare the combined fan current with the header limit in the motherboard manual. A powered hub may take fan power from the power supply instead, depending on its design.
That is one possibility, not a diagnosis. A single faulty fan or cable could also cause trouble, so the damaged board still needs inspection.
pOstcardFromPayroll:
Check the hub wiring too. A splitter without separate power and a powered hub don't necessarily put the same load on the motherboard header.
I wouldn't start by probing a live header with a multimeter. After visible burning, a repair technician or the manufacturer can assess the board without you having to power up a potentially damaged circuit. The CPU may be fine, but nobody can promise that without checking the system.
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~no+more!backtracking:
Should I send photos of the connector as well as the scorch mark?
ALSO.on.page:
Yes. Include both ends of the cable and any splitter or hub involved, plus the motherboard and fan model numbers if available.