I agree that the component mainly holding performance back in those games is likely the FX-6350. It's a six-core CPU, and actually only came out about four years ago, but while it still has okay performance in heavily multithreaded software, its performance per core is kind of low, and those games likely rely on high single-threaded performance. There aren't any CPUs available for that motherboard that are much faster though, so an upgrade would require at least a CPU and motherboard. And as was already pointed out, if you're going with the most recent generation of CPUs, you'll also need DDR4 memory.
It would be a good idea to open the case and check what kind of power supply it has, to determine whether it might be worth replacing or not. It should say on the side of the PSU what brand and wattage it is.
Herc08 :
I would have paid no more than $250, especially consider the age. 5 years ago, maybe $350. But now, no more than $250, and I would try to talk them down as much as possible.
Hah! I would disagree with this though. Five years ago, neither the GTX 960 nor the FX-6350 even existed. The 6350 came out in 2013, and the 960 came out in 2015. Five years ago, a computer with those specs would have been far more valuable. Even just a graphics card with similar performance to a GTX 960 would have been $400 in 2012. : P Looking at today's prices, I don't think $450 was necessarily "bad" either, although perhaps not ideal for gaming. And are we even talking USD here? I notice the dollar sign is after the value, which might indicate to me that the OP is in a country other than the US, with different pricing and exchange rates.
In any case, going by USD, a GTX 960 is generally faster than a 1050 Ti, which is around a $150 graphics card. And while an FX-6350 might not be ideal for newer games, it is still a $100 processor new, and the motherboard is over $75. Then around $75 for a 2TB hard drive, and another $50 for 8GB of DDR3, and you're looking at $450 right there. Add in a case, power supply and Windows license, and a computer with those components would probably cost close to $650 to build new today. So I wouldn't say that $450 was necessarily an outlandish price. And that's without any components like keyboard, monitor, and so on, which weren't mentioned, and I'm assuming weren't included. I highly doubt you could build a better PC than that for $450 though, at the very least.