minimum specs to replace 3 yr old PC

This is the specs of my current PC:

i5-2400
AS Rock H61 motherboard
4 GB DDR-3 1333
2x 500 GB HDD
HD 7850
22" 1680x1050 screen
Rosewill R102 mini tower (max gpu length 9.1 inches)
Corsair 500W PSU

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I'm planning to use a portion of my tax refund to replace this system, this computer would be 'handed down' to a relative or turned into a Linux play box. What I'm wanting is what you consider the minimum upgrade to make it worth spending the money on a whole system, not piecemeal upgrades to this one. Where I would see SIGNIFICANT gains in capability.

I have no plans for multi-screen gaming -- my computer desk is not big enough to handle more than just one screen
 
With the i5 2400 still being in the top tier of CPUs for gaming, I wouldnt suggest any upgrade there. Even faster RAM wouldnt make a difference. If you want it to feel like a new PC, put a 290x or 780ti in there. Youll notice a difference, no reason to upgrade anything else. In my opinion anyhow. I know you said no piecemeal upgrades, but IMO, you dont need to upgrade anything, you wont see a difference unless you upgrade your GPU. Might want another 4gb as well.