This sounds like a bad connection from the CPU cooling fan on one specific pin. The speed of the fan is sent to the mobo on Pin #3 of the connector that plugs into the mobo CPU_FAN header. Most mobos do some special monitoring of that fan's speed signal, unlike the ones for the case. IF they fail to get a speed signal, SOME (maybe yours?) will issue a brief warning, then shut everything down immediately without even waiting for the temperature inside the CPU chip to heat up. This is to prevent rapid overheating and potential CPU damage.
So, first take a close look at the way the fan is plugged into the CPU_FAN header. Watch for a loose or broken connection. If it looks OK, gently unplug it and then plug it back in again, several times. IF there happens to be oxidation on the metal contacts, this action may "scrub" them clean and re-establish good contact. Then try to boot your machine.
If that does not work, you could try another type of test. Interchange where you have plugged in the CPU cooler fan and one of your case ventilation fans. That is, plug the CPU fan into a SYS_FAN header, and the case fan into the CPU fan header. Start up for a short time. If it starts and stays running, then the CPU_FAN header is now getting a good speed signal from the case fan temporarily connected to it. Next, quickly check what the BIOS tells you about the speed of the CPU cooler that is actually connected to a SYS_FAN header. Does it have a speed? If not, the fan is failing to send a speed signal to the mobo header. Shut down and reconnect fans properly.
You could do that second odd test for a short running period. It's not ideal because temporarily the actual cooling of the CPU is based on the temperature of the mobo, which is not right; however, there will be SOME CPU cooling for the short test.
If that test indicates that the actual CPU cooling fan is failing to output a speed signal, you MAY be able to figure out why (look for a poor connection somewhere), or you may just have to change that fan.
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