Help with building a new PC

Hey guys, I plan on buying a new PC (gaming) with a $700-800 budget. The reason is that my current PC has multiple issues like video issues, slow down, blue screen, etc. I could pay someone to figure out what exactly is the problem or post on here for more help or what have you, but I'd rather just buy a new PC.

I will be blunt, I have no idea whatsoever about what works together or what the best parts are for the budget I have. I'm coming to you guys because you have helped me before on this, quite successfully, so I trust the people here.

This is the current PC I have right now:

8GB DDR2 (I believe)
GTX 570
i5 2500k
GA-Z68A-D3H-B3

The reason I give these specs is I would appreciate it if after you create some sort of build for me, that you'd let me know how it compares to the current PC I have power wise. I need to stick to the $600-700 budget regardless, but the information would be nice to know.

I am keeping the case/hard drive/monitor/cd drive I have now.

Thanks to anyone who helps me out, I really appreciate it and I really am lost when it comes to building these things so I am very grateful to anyone who takes the time to put together something for me!

(I apologize if this is the wrong section, I just assume hardware is where you post something like this)