I have a PC with an Intel® Core™2 Duo Processor E4300 - I ran CPU-ID on it, and here are the results:
Is this capable of running Windows 64-bit?
Yes, all Core 2 Duo chips are 64-bit capable, that is includes the EM64T feature. Of course, if your running a 32-bit OS then it'll be no different then a 32-bit chip, but if you put a 64-bit OS on your system the Core 2 Duo chips will handle it properly. So yes it is capable of running 64-bit Windows.
however please note;