Core 2 Quads are Socket 775, 771 was for Xenon's. While a 771 CPU can be adapted to run in a 775 motherboard, I've never heard of a 775 CPU working in a 771 motherboard.
You will need to check the CPU compatibility list for your motherboard to see what the best CPU you can run is. If you don't know the motherboard make and model, you can run a program like CPUz and get the information.
You can buy used CPU's on eBay, I bought a couple C2Q Q9550's (Socket 775) from there and they have been running great for over a year now. Even OC'd one of them. Buying a used CPU isn't ideal, but you can get a decent deal...but it's a gamble on how long it will last.