core2duo @ 2Ghz is really, really slow. you could even pick up a haswell pentium @ 2.7Ghz and it'd outperform it by more than twice.
an i3 upgrade would be the cheapest and reasonable path, an i5 would be a budget stretch tho.
on the other hand, if you could get your hands on the overclockable pentiums then those could potentially outperform a cheap i5 for less costs.
edit: PS4 or consoles in general are a waste of money, most of those who pick them up either has too much money, or not enough money to buy a gaming PC.
i mean think about it, you could play most of the console games in a PC, some of those games can even be played at a much better graphic quality.
only a handful of games aren't ported to PCs or are badly ported, sadly theres no PS4 emulator yet but that doesn't matter much though.