As stated we need to know the exact CPU you have installed. There were many Core 2 Duo's and only the High End ones will be able to handle the 7870's. No matter what your performance will be limited due to the 800 MHz speed of the ram.
Also, like stated above, your PSU needs to be powerful enough to handle the GPU. Please state your exact PSU model and wattage. A model number would be best.
Yes for sure your System is a socket 775 as ALL Core 2 Duos' were LGA 775 socket. Many of the boards were PCI-e x16 2.0 during there run.
If you choose to get a new MB you will also need a new CPU and ram as all newer boards as of LGA 1336 and AM3+ are all DDR3 boards. There is a new standard out now that is just starting to be phased in and...