You are correct, you would have to change the CPU and motherboard. Depending on the power requirements of the new board, you might have to upgrade the power supply also.
If your current system is older, you will also have to deal with issues like making sure the current box will allow enough air flow for the additional heat, physical locations of USB connectors and graphic card compatability. Rather than try to navigate all of the differences between an old machine and a new 64 bit, I'd get a new box and start from scratch. You can still save some money by putting it together yourself but the supplier could put together a package designed to work together that would let you avoid all of the compatibility issues.