Question : Problem: Will this cpu work with vista 64bit?

Will a P4 2.66ghz, LGA775, 533Mhz FSP, 1MB L2 Cache work with Windows Vista 64Bit?

Answer : Problem: Will this cpu work with vista 64bit?

Also see this chart, and the last 3 entries matches Your processor, and only one of them supports the EM64T feature:

http://www.intel.com/products/processor_number/index_view_p4.htm

You should see the exact processor model or use some software to get the type of it. I'd recommend this one:
http://www.cpuid.com/cpuz.php
http://www.cpuid.com/download/cpu-z-135.zip