Your motherboard uses a 945gc chipset. Most of those boards don't support the newer intel core2 duo cpus, such as the e6600. I would leave it alone. Either sell it intact before the board or power supply fails, or use it for a spare. It isn't worth putting any money into, and a board change will mean you will need a new windows coa number. The windows operating system is tied to your board. Microsoft might send you a new coa, but often they will tell you to call emachines. Emachines doesn't supply bios updates that I know of for a cpu change, and your chipset is so old, it won't do any good.
The only one officially supported is the one it came with.
And just like oldie said, even though it is 775, it likely will not support anything non-pentium 4. My brother built his own computer a few years back with a P4 and a 775 socket. It doesn't support anything better than the P4 with hyperthreading.