The BIOS on your motherboard will need updating to support the CPU. Normally the system would not boot at all but if your board will support a Core 2 Duo then that may explain it. The chip you are using is two Core 2 Duos on the same chip and sharing the cache so the BIOS still sees it at that level. To get it to see the chip as a "Quad" or in this case two Core 2 Duo CPU's you need to update the BIOS.
I found out that my motherboard brand is 'ESonic' and I can't find the motherboard model and it seem like they don't have any official website at all.
But there's a sticker with the word "945GCFBBL"
The design similar to this
Can we mod the BIOS or use any trick to enable the quad core?