Problem booting up

Try this, open up your computer casing and remove your RAM stick and the power connector of the harddisk. Now turn on your computer. Do you hear any beep sound? If yes, turn off your computer, put it back but before it use a pencil eraser and rub the contact point of the RAM. Turn it back on and see if you computer can boot up.
If still not success, remove the graphic card (if your computer have a graphic card). Turn on the computer, you should hear a long beep sound. Again as step above using the eraser and rub the contact point of the graphic card. Place it back and turn on your computer.
If the step above can boot up your computer, turn it off and then connect back the power to the harddisk.
If still not successful, try to change the RAM or the graphic card.

This is a well-documented issue on GX280 Optiplex machines for which there is no permanent fix - at least there is not one I came up with or found elsewhere. The symptom is that after power on, the CPU fan spins faster and faster until it tops out at rather impressive RPMs. Swapping power supplies, memory sticks, CPU, the heatsink and fan assembly, or adding more heatsink grease does not make any difference. There are no beeps, no video, nothing. The problem is related to a CPU temperature sensor, and some machines may display a message on the screen stating so.
Through various trial and errors I was able to make almost any motherboard with this symptom boot up. A rather significant downward pressure applied on the top of the fan vent will make a system boot up and run for days, but the pressure has to remain in place or the system will freeze instantly. This pressure has to be applied not on the top of the entire fan assembly but just on the vent side, in a way that the heatsink will not make good contact with the CPU on the side opposite of vent. What I do is I place a 1/2" tall object at the top of the fan casing right at the tip of the vent and force the case closed. The PC will boot and work as long as the case is closed and the pressure is there.
I have no idea what the pressure on top of the heat sink vent really does. I suspected that maybe the CPU contact pins become elastic and deform over time. I tried carefully and tediously bending all of those pins up a bit to create a better contact point, but that did not work. I also removed and measured capacitors near the voltage regulators for capacitance, and all typically measure near their advertised values. I haven't seen a motherboard with popped caps and this racing fan issue concurrently, but this doesn't mean the symptoms are mutually exclusive; it's probably just a coincidence.
I'll keep looking and trying to find a fix for this issue. We have a small pile of motherboards with this identical issue at my workplace, and when/if I find a solution I'll be sure to write about it.
Good luck!