Go to control panel-> Hardware and Sound -> Device manager (under Devices and Printers -> Processors and then it should tell you at the very least the name of the processor, but it should tell you how many cores by posting the name of the processor the amount of cores you have, so if you have 8 cores the name of the processor should come up 8 times, as well as 2 times for duo's and 3 times for tri's, etc....
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Open up as in open the computer? No that wouldn't work because the name is on the processor and that's covered by the heatsink + fan, so unless you wanna remove that and put it back on, which I highly advise against doing, then the only way i currently know how is the way I described, or you could go Google CPU-z; download it and it'll tell you everything you need to know about your processor.
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Not even Death will save you from Diablo Bunny's Cuteness!
You can also check this program CPUZ whatever your pc is old or new it will give you many details not only about your cpu but also what type of motherboard and ram you have.
run
DXDIAG
should display all relevant hardware, including your CPU and its' cores.