The Intel D945GTP motherboard supports Pentium 4, Pentium D, and Celeron D processors — it does not officially support Intel Core 2 Duo processors.
The 945G chipset was released before Core 2 Duo and may not have the proper VRM or BIOS updates needed to run them reliably. Even if some users have tried workarounds, official compatibility is not guaranteed.
If you want to use a Core 2 Duo, a motherboard with a G965, P965, or later chipset would be a safer choice. If you’d like, I can suggest compatible boards!