You should be able to do all that for around $800 without too much trouble. For $1500 you can build a bleeding edge gaming computer if you want to. For Example I put together a AM3 gaming rig with Triple SLI 275 GTX and 8 GB RAM a fancy case, big time PSU and dual boot with Vista and XP both and the cost was just a hair over $1600 - before rebates..... It was made to game at 5400 x 1050 resolution, so you could build something to play whatever you want at a 20" LCDs res. for far less.
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