On it. Posting in a minute. Edits will be ongoing.
If you have an HDD, that'll help a lot.
Let's see if this is at all possible on Newegg, assuming you don't want a single-core HTPC. "Fast" is not going to happen, though.
-$60 X2 250, dual-core 3 ghz
-$80 Hitachi 500gb
-$55 ASRock 880GM-LE, micro-ATX
-$35 Rosewill case, dual fans: http://www.newegg.com/Product/Product.aspx?Item=N82E16811147123
-$35 Corsair 430W PSU ($45 before rebate). You are not allowed to go any cheaper on this.
-$21 Kingston Value 1x4gb RAM, 1333mhz
-$19 Asus ODD: http://www.newegg.com/Product/Product.aspx?Item=N82E16827135204
$305, without a GPU. That means basically no gaming. What do you mean by "gaming," though? Online gaming? You're not going to get Battlefield out of this thing without another $80 or so at the very least.