Buy a new PC or upgrade parts?

[Rias]

Hey guys,

I've been thinking about upgrading my computer for a while now. I think it's getting quite old. I bought it almost exactly 8 years ago, but I have upgraded the RAM and upgraded the graphics card because the old one broke due to bad maintenance on my part.
I bought it with advice from this forum, back when I was really into games. I still really enjoy them, but not as much anymore due to lack of time. If possible I would prefer upgrading as I see it as the cheaper option, but I understand buying a new computer would probably be better since this one is quite old.

In any case, here are the specs:

Sapphire AMD Radeon HD 6800 1GB Graphics Card
Intel Core i5 750 2.66Ghz
MSI P55-CD53 Intel P55 (Socket 1156) DDR3 Motherboard
Corsair Vengeance DDR3,1600-16GB
Western Digital Caviar Black 1TB SATA-II 32MB Cache
Corsair TX 650W ATX SLi Compliant Power Supply
Antec 300 Three Hundred Ultimate Gaming Case - Black

All advice welcome, thanks a lot for your time and help!

 

[Rias]

Hmmm, not looking to spend more than 800 euros/700 pounds. For that amount I would have to do some saving, and with the Christmas period coming up that wont be this month.. Haha
If I could keep it at a few parts for less money I could get to shopping right away.