Strange processor issue

I have a Sony Vaio 2.4Ghz I got in 2003. I recently built another pc for my daughter using the same era MB and processor. I got the new (used) 2.4Ghz processor on ebay. I put it in and it didn't work. I then took the processor out of my Vaio and put it on the new pc. The Vaio processor worked. I took the processor I got on ebay and put it in my Vaio. It works but at only half the processor speed (shows up as a 1.2Ghz).

I thought the processor might have been bad so I tried three more and they all worked the same way. It seems like the Vaio processor will work on any motherboard BUT only the Vio processor works on the Vaio motherboard.

Are there different 2.4Ghz processors out there that have compatibility issues with some motherboards or something? I can't figure this out.