Odds are it's a socket 478, not a 775. Even it it were a 775, I doubt the mobo could handle a Core2Duo.
If you want to keep your RAM, you can go with a Pentium D or an AMD socket 939. Both are older tech, but cheap.
You can go with a Core2Duo build, but all you'll be able to use would be your hard drive. You may be able to re-use Windows if it is an retail copy, other wise you'd have to replace it as well.
Either way, you will have to replace your power supply. And if your system is a pre-built (Dell, HP, Gateway, etc) you'll need to replace the case as well.
My Rig: SABLE
Antec 300 Illusion / Antec EarthWatts EA650 650W / EVGA GTX 760 2GB
AMD FX 8320 x8 Black Edition / Gelid Tranquillo / MSI 970A-G43
Sandisk Ultra Plus 128GB / Samsung 840 120GB / WD Black 750GB / WD Green 1TB / WD Red 3TB
G.SKILL Ripjaws 2x2GB DDR3 1600 - Crucial Ballistix Tracer 2x2GB DDR3 1600
Win7 Ult 64-bit - Func MS3 Mouse - CM Storm QuickFire Rapid Mech Keyboard
R.I.P. Danny L. Trotter
... 14 Nov 1945 - 4 Sept 2009