My computer turned off this morning. I found one of the pins of the power connection to the motherboard for the CPU burnt. (This MATX motherboard has a separate pair of connectors for the CPU: 12V, 16A.) Fortunately I have another PS. I find nothing in the logs.

Did the CPU draw too much power?

It is possible the CPU drew to much power as well as the connector pins might of been oxidized causing increased resistance and heat buildup. If the corresponding pin/socket on the motherboard is also burnt you still could have a problem. Does the motherboard still work?

clean (both sides of) the connector to restore the connection, probably that will be enough.

It does, the import of my comment that I had another PS.

Not really cleanable because it's recessed inside its plug. The whole plastic portion of that wire on the plug is burnt. It's not just dirty.

After thinking about it, the CPU power has 2 12V wires; 2 because it can draw up to 16A and that's more than one wire can carry. (The MB has 3 and it's rated at 12A.) If one wire failed, all the current would go through the other. Neither of the ground wires is burnt, which would be the case if they're both good. So that's a sensible guess about what happened.