The Intel socket 775 chipsets are now obsolete (not exactly sure what date but I guess would be in 2009 when socket 1156 came out.)
NON TECH SAVVY SUGGESTIONS BELOWIf you don't know what you or anyone else is doing when building a computer, go buy a new one for 500 and it will save you the hassle of figuring out what goes where as well as lasting for another 6 years. If this applies to you, please ignore the ridiculous amount of text below.
TECH SAVVY SUGGESTIONS BELOWFrom what I know, the Core 2 Duos are the last processors to be developed on that socket and therefore the most powerful processors ever developed on that socket. I don't know about you but if you still want to use mainboard, I suggest looking for the most powerful CPU developed on a 775 socket which is located here, although I'm not sure if your board supports it (I'm pretty sure it does).
http://www.tomshardware.com/forum/288597-28-what-powerful-socket-processorNow If you want to upgrade both motherboard and cpu you can find it online in bundles starting from 100 bucks, I personally recommend Micro Center since they have the best deals.
Since you don't know what format of RAM you have whether it be DDR2 or DDR3 and may be wondering if it's still useable in the combo, compare yours with this picture below.

There are a lot of compatibility specs for the motherboard so check out the technical specifications to see if your current RAM is compatible with it.
Another thing to note is wattage, if your new board and processor is taking much more power than the previous one and your computer randomly sputters out, upgrade your power supply.
Once you have rebuilt your computer, you will need to remove previous motherboard drivers and install new ones, although I'm not sure about Microsoft's OS as I read though an article somewhere claiming that the OS will lock if they find the parts to be different.
~Trust me on this one as I'm a certified technician (A+ cert)~