Motherboard upgrade question

No. Your processor is LGA socket 775. LGA 1155 is a whole different series of motherboards made for sandy bridge, and ivy bridge. You'll have to get a new processor, RAM, and motherboard if you plan on getting LGA 1155 motherboard.

You can find some motherboards for sale with the 775 socket, but they are few and far between. Some do support DDR3, but only up to 1333Mhz, which is on the low end of DDR3. Buying a new 775 motherboard will be your cheapest solution, but your Operating system is tied to your motherboard, not hard drive, so be prepared to buy a new OS with which ever route you decide to take.

If you considering redoing the system (minus PSU,HDD, case and disk drive) I'd recommend this for a budget.

CPU:Intel Core i3-3225
http://www.newegg.com/Product/Product.aspx?Item=N82E16819116774

MB:MSI Z77A
http://www.newegg.com/Product/Product.aspx?Item=N82E16813130653

RAM:Crucial Ballistix Sport 8GB
http://www.newegg.com/Product/Product.aspx?Item=N82E16820148543

OS:Microsoft Windows 7
http://www.newegg.com/Product/Product.aspx?Item=N82E16832116986
Total cost $393

It might be worth it to upgrade everything else depending on how old the system is.
Add another $150 if you want to upgrade everything else(PSU,HDD,Case, and disk drive)

No. Core2Duo and Core2Quad are "socket 775-only" processors. It's the end line of 775 socket, you can't upgrade further without changing motherboard and thus socket.
You CAN get a "775 socket"-motherboard that has DDR3 on it's board though, so you can still upgrade your memory without changing socket and processor just fine .
I can give you a couple of recommendations on particular models, if you want.

Thank you everybody that has replied, I have decided to postpone my system upgrade simply because I can work with what I have now and I'm not prepared to dos out £100 on a new OS licence! I hate it when its like that, but any way, thank you. This has been my first thread on toms hardware, and I got a quick and easy to understand responce, thank you!

Oh well...
You are always welcome anyway.