You are probably out of luck in this case. There are no dual core CPUs on Socket 478. You may be able to get a slightly faster Pentium 4, say 2.8 or 3.0 GHz maybe, you would have to check your mobo's manufacturer's website for a CPU support list for your particular motherboard, it's possible your current CPU is the best you can get.
I would seriously consider a new build at this point, Socket 478 has been dead for a long time, and even a cheap bottom of the shelf computer that you can find at Best Buy or Wal Mart is vastly superior to that old rig. There's no sense in pouring money into technology that is extremely obsolete at this point.