Guess what, I succeeded. If you weren't here to read the previous post it is at "THIS LINK ". Although I didn't get an actual core 2 duo processor, I could have. I spent ~$430 on my whole machine. The specs are this.

-Pentiuim D 2.66GHZ 2MB Cache
-260GB Hitachi SATA 3gb/s
-ECS 945GCT MOBO(Comes with on board Intel video that plays most all newer games)
-Sony DVD/CD R/RW Drive
-Rosewell Computer Case
-2GB Super Talent RAM
-Wireless Keyboard and Mouse

In short, this was a build I was very proud of. This would not have been possible without the donation of a 19" flat screen LCD. The price would have jacked up another $200 but is way cheaper than any computer you would buy from Best Buy or such. I could've afforded a Core 2 Duo with the spare cash, but I'm perfectly fine with this Pentium D. After all, it has two cores.

So, can it be done? No. Can you make a comparable machine? Yes.