Checked. The CPU fan connector sits very firmly. On start, CPU fan only jerks and doesn't spin, but I am not sure if that indicates anything because my main PC's CPU fan doesn't start spinning until few seconds into POST.
The case fan spins steadily until system shuts off.
This may be the root of your problem. You report that the CPU cooling fan does NOT start up at all, and then the system shuts down. The normal operation would be for it to start up at full speed within a second or two of power-on, and then slow down as the temp control loop begins to regulate according to the measured CPU temp. With NO fan operation, three possibilities occur:
1. The mobo is monitoring the CPU fan speed signal, sees no fan operation, and shuts down right away - that is within a few seconds. IF you have a PZO unit attached to the mobo it will send out an audible beeping alarm, but you won't hear that if you have no "beeper" unit.
2. The mobo does not have a system to shut down based solely on CPU cooling fan speed signal, but of course it does monitor the CPU internal temperature. With no CPU cooling fan, that temp will rise quickly to the alarm point and the system will shut down. Usually this takes 5 - 10 seconds,
3. You have set the options for the CPU fan control system in BIOS so that is does NOT monitor the fan speed. This becomes option 2 - it will still shut down based on actual CPU temperature.
So for whichever reason, your CPU cooling system is not working and needs repair. Check these:
1. Try to turn the fan gently with a finger or a pencil. If it is stiff or does not turn at all, you should replace the fan.
2. If it turns freely and glides gently to a stop, the bearings are OK. Try disconnecting the fan and connecting to it a source of 12 VDC, using the RED (+) and BLACK (-) wires of the fan (NOT the Yellow). Maybe a car battery, or some other simple source. Actually, any voltage over about 8 VDC will do to start it, but it takes the full 12 VDC to run at full speed. If the fan runs properly this way, its motor is OK.
3. Although the fan appears to be connected properly to the mobo, try disconnecting it there and re-connecting, several times. Sometimes with age the pins in this connector get coated with metal oxides that interfere with the connection, and this action will scrub them clean so it works again. Then try starting your machine to see if it works.
The other possibility, as others have suggested, is that I'm on the wrong track and the real cause is some other component that fails, quite possibility affecting the power supplied to the board, and it fails but retries for this reason. This could be a faulty PSU, a faulty portion of the voltage regulator circuits on the mobo, or an attached peripheral component that draws too much current from its supply lines.