Here is the compatible with your system. https://ark.intel.com/content/www/us/en/ark/products/29765/intel-core-2-quad-processor-q6600-8m-cache-2-40-ghz-1066-mhz-fsb.html Id then recommend a bios update before to ensure compatibility.

please list your CPU model.

I can try finding available CPUs that way.

The answer is quite simple:  No.

No i7 was never made around that time.