Let us know the Motherboard Model. I believe the other fans in your Case is running because you should have connected them to a molex power connector rather than the three pin (Fan Controller) from your motherbard.
What do you mean by Boot Process Does not start up? If you dont see a BIOS screen on boot then it should be a problem with your motherboard.
First check whether you have connected the 24 (20+4) PIN power connector properly to your motherboard.
Then when you Switch ON your PSU a LED (Possibly if an Intel Board) should glow on the motherboard which is the indication that the motherboard gets the appropriate power. Even if the above things dosent start your processor then there should be some problem with your motherboard.
Check and let us know .
The MOB is Gigabyte GA-EP45-UD3P. The power supply fan was running, the back panel fan was running (connected to power supply) and the video card fan was running. Also the MOB leds were lit, 4 green and two red. There clearly was power getting to the MOB. The CPU fan was plugged into a 4 pin socket on the MOB. I tried to get a voltage reading on that socket but I was unsuccessful. Ultimately I decided to return the MOB for a replacement. I am still concerned that the CPU fan might have failed. The CPU is an Intel core 2 duo E8400. Thanks for your response.
From what you have given I assume that the motherboard gets the sufficient power supply. But CPU fan doesnt have anything to do with the boot process. Even without a CPU fan the processor can be up and running, The only problem being it will heat up worsly without a fan and die soon.So try to check the processor-motherboard assembly once again. You should get the BIOS even if CPU fan fails. Try to remove the CMOS battery for some time and place it back. Try booting for any luck.