If you suspect you may have an issue with the CPU itself, you might try downloading and running the Intel Processor Diagnostic Tool. Click on the following link for more information: http://www.intel.com/support/processors/sb/CS-031726.htm
Since your system seems to boots up, you might run the diagnostic tool before calling the CPU defective. The tests run by the tool should help you determine if there is a hardware issue with the CPU. If not a hardware issue with the CPU, there may be a software error with the OS or a driver issue of some sort, or it may be a problem with some other hardware in your system.
If you have determined that the CPU is bad or you require more assistance in troubleshooting the processor, you might try contacting Intel support: http://www.intel.com/support/feedback.htm
Intel Customer Support
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