we need a bit more info. I believe that intel introduced x64 bit extension very late i the in the p4 development cycle. If your motherboard has a socket 478 then NO. If it uses the LGA 775 then prolly yes.
I tried CPU-Z and it didn't really say outright if my system was 32 or 64 bit. I have an Intel Core 2 duo E6400 Socket 775 LGA with a P5N32-SLI-SE-Deluxe.
Does the CPU and the motherboard have to be 64bit to run a 64bit OS?