Well, not that quick ... My old computer (circa 2004) can still play some new games (AMD AthlonXP 2500+ @ 2.26 GHz, 1 GB of RAM, GeForce 7600 GT), though the GPU has been upgraded since it was built.
Of course, I've had a few computers since then and my latest has no trouble whatsoever playing anything.
If your computer is over 3 years old, it is either going to require MAJOR upgrades or replacement to keep up w/ modern games. At 7 years, I'd say complete replacement is the only option worth considering.
What game(s) are you trying to play and what are your computer's specs ?