You can download a free application like Everest Home Edition that will tell you the make and model of all of your hardware and its properties. If you decide to use Everest, go to the Motherboard tab and then again to the Motherboard sub-section and look for the Front Side Bus Properties and the Bus Width. That will tell you if your motherboard is 32-bit or 64-bit capable. Odds are good that if it came with a Core 2 Duo, it is 64-bit capable. Similarly for your CPU, you can go to the Motherboard tab and the CPUID sub-section and look for the 64-bit x86 Extension (AMD64, Intel 64) box to be checked and marked Supported.