product key from old pc to new

Unless you picked up the Retail copy, you can not.

OEM copies of Windows are locked to the first system(motherboard) they are activated on.

Simply put, for legal reasons, you should be purchasing a new license for Windows on the new PC.

If you bought retail then you can just remove Windows from the old system and install it on the new system with the DVD(and COA) you have already.
 
Physically, you can. Windows OEM keys are hit and miss when it comes to the authentication triggers. Ive had Vista OEM trigger on a HDD change, while completely upgrading (incrementally) a Win7 machine and not had it trigger. Even with the Vista experience, I simply called MS, explained that I changed my HDD due to failure and they gave me the re-activation code over the phone. Its hard to define a "PC" common sense says that the mother board would be the true machine, but one could argue that the case itself defines the machine. This is why they are so lenient when it comes to it.
 
MS defines the system as the motherboard. They are "lenient" depending on who you get.

From MS (http://www.microsoft.com/oem/en/licensing/sblicensing/pages/licensing_faq.aspx#fbid=HRiAu5Oh10E)
Q. Can a PC with an OEM Windows operating system have its motherboard upgraded and keep the same license? What if it was replaced because it was defective?

A. Generally, an end user can upgrade or replace all of the hardware components on a computer—except the motherboard—and still retain the license for the original Microsoft OEM operating system software. If the motherboard is upgraded or replaced for reasons other than a defect, then a new computer has been created. Microsoft OEM operating system software cannot be transferred to the new computer, and the license of new operating system software is required. If the motherboard is replaced because it is defective, you do not need to acquire a new operating system license for the PC as long as the replacement motherboard is the same make/model or the same manufacturer's replacement/equivalent, as defined by the manufacturer's warranty.

The reason for this licensing rule primarily relates to the End User Software License Terms and the support of the software covered by those terms. The End User Software License Terms are a set of usage rights granted to the end user by the PC manufacturer, and relate only to rights for that software as installed on that particular PC. The system builder is required to support the software on the original PC. Understanding that end users, over time, upgrade their PCs with different components, Microsoft needed to have one base component "left standing" that would still define the original PC. Since the motherboard contains the CPU and is the "heart and soul" of the PC, when the motherboard is replaced (for reasons other than defect) a new PC is essentially created. The original system builder did not manufacture this new PC, and therefore cannot be expected to support it.

Again, this is not to say MS will not do it(they are honestly quite good to deal with), but if they choose not to, they have that right.