The BIOS (EFI) is part of the logic board so if you are swapping the logic boards the new board should have the needed firmware already present.
If you are trying to upgrade your CPU in this system then you'll need to first get it running with the correct CPU first so you can check to see what the systems firmware is currently and if the logic board its self is in good health. Here is the link to check your system: About EFI and SMC firmware updates for Intel-based Mac computers.
Here's a link to someone who has achieved this: CPU upgrade 2.0GHz to 2.8Ghz ( C2D Extreme X7900 ). They needed to swap out the heat sink.
Given the other limitations this system has I'm not sure its worth the effort. It can only support 6 GB of RAM and while it can run El Capitan 10.11.x I would recommend staying with one of the older OS's as the OS footprint is smaller. Also keep in mind MacOS Sierra is not supported on this older system either.