All of the "no" answers are wrong. Microsoft says that one license is good for one installation of Windows, be it x86 or x64, even if it is an OEM license. The keys work for both 32 and 64 bit.
Granted, you have to completely remove the 32 bit version from the old hard drive (format) and install the 64 bit version only on the new setup. As long as the motherboard isn't changed, you are good to go.http://social.microsoft.com/Forums/en/genuinewindows7/thread/718fa596-c90b-4070-b484-03bd9478a233