No. the clothes dont make the man. a current-gen game could have ps2 graphics but if it has an excellent halo-quality/red dead redemption quality storyline and amazing revolutionary gameplay and an amazing orchestra background music then its just as good as a game with awesome graphics. i dont mind the graphics of old ps2/ps1 games, i mean we didnt mind because we didnt know what 1080p would look like. graphics are just a bit of visual flair, sure i would like a cool panoramic view of the surrounding mountains in stunning hd, but i can get the same quality in a "average" graphics game.
if you want the cheapest.. buy a 20-40$ RROD Xbox 360 (probably jaguar/falcon etc.) off craigslist or ebay and find someone to fix it. reasonable repair prices for an rroded first-fourth wave xbox 360 is around 30$-50$