You should really check these things first or consult the motherboard documentation which lists in great detail what the board supports
Get yourself a new manual if youve lost the one that came with it
And to answer your problem , no you cant have a quad core
your specification says
"CPU - LGA775 Socket for Intel Core 2 Duo/ Pentium D/ Pentium 4/ Celeron D/ Celeron Processors with 1066 MHz FSB - Supports Intel Hyper-Threading Technology "
It would say "Intel Core 2 Quad" if you could
Try powering it up and it will probably either:-
b)Spark and set on fire if theres not enough cooling
c) Cause a power cut , Quad cores take more power than the boards designed to support , otherwise they would have said i t supported quad cores.
d)Fry up the motherboard , making it useless
e)Fry up the processor , making it useless
f) all of the above