Using the specific MB model number, find the MB's online product page and see the CPU support list to find which processors are supported by which BIOS versions. The old Intel 945 chipset supports Pentium D dual cores and depending on the model, some C2D's may be supported.
Yes, the 945G Chipset supports dual core Pentium D and some Core 2 Duo CPUs.
If your motherboard supports these CPUs is another story.
Check your manufacturers product page and see the CPU Support List for your motherboard.
If the CPU you want to upgrade to is supported, make sure your BIOS is updated before installing it.