Here ya go for ~$600 B.R.
CPU - $99 shipped!! Not the 940 like you like, but to get the most "Gaming" power you need a good GPU for that, so that is why I went with this CPU. It's OC's (easily) to 3.6-3.8 gHz, which is plenty for gaming needs at this point! If you want a Quad core than I'd suggest the Athlon II x4 620 for the same $.
AMD Phenom II X2 550 Black Edition Callisto 3.1GHz 2 x 512KB L2 Cache 6MB L3 Cache Socket AM3 80W Dual-Core Processor - Retail
http://www.newegg.com/Product/Product.aspx?Item=N82E16819103680
GPU - $163 shipped!! There are better GPU's, but for the $ right now it's hard to beat!
HIS H577FM1GD Radeon HD 5770 1GB 128-bit GDDR5 PCI Express 2.0 x16 HDCP Ready CrossFireX Support Video Card - Retail
http://www.newegg.com/Product/Product.aspx?Item=N82E16814161317
Mobo - $88 shipped - $10 MIRc = $78!! Hard to beat for the $!
GIGABYTE GA-MA770T-UD3P AM3 AMD 770 ATX AMD Motherboard - Retail
http://www.newegg.com/Product/Product.aspx?Item=N82E16813128392
RAM - $100 shipped! It has Cas7 timings and runs at stock voltage (1.5v) What else do you need??
G.SKILL Ripjaws Series 4GB (2 x 2GB) 240-Pin DDR3 SDRAM DDR3 1333 (PC3 10666) Desktop Memory Model F3-10666CL7D-4GBRH - Retail
http://www.newegg.com/Product/Product.aspx?Item=N82E16820231276
Case/PSU combo - $90 shipped!! Hard to beat for this price. You get the Antec 200 case/400w ECO PSU (30A on the 12v rail). Plenty of power for the 5770. The PSU does limit your upgrade paths a bit, but 30A on the 12v rail is NO SLOUCH!
http://www.newegg.com/Product/ComboDealDetails.aspx?ItemList=Combo.319122
HD - $55 shipped! Good solid and fast for the $!!
SAMSUNG Spinpoint F3 HD502HJ 500GB 7200 RPM 16MB Cache SATA 3.0Gb/s 3.5" Internal Hard Drive -Bare Drive
http://www.newegg.com/Product/Product.aspx?Item=N82E16822152181
DVD Burner - $30 shipped!! Comes with the software to read/burn DVD's!!
LITE-ON Black 24X DVD+R 24X DVD-R SATA Black 24X DVD Writer - Retail
http://www.newegg.com/Product/Product.aspx?Item=N82E16827106334
Total - ~$625 shipped - $10 MIRc = $615!! Now if you still want the 940 (don't recommend for this budget) you'd have to drop down on the GPU side (4770 for $117 shipped???). It's up to you, but having the best GPU you can afford will give you the better overall gaming experience. Most games only take advantage of up to 2 cores. This doesn't mean that 4 cores is a bad idea, but it's something to think about. If you want the 4 cores, than the Athlon II x4 620 is a very good buy and will fill that need and won't break the bank/budget.
Link to 4770 ($117 shipped!):
XFX HD-477A-YDFC Radeon HD 4770 512MB 128-bit GDDR5 PCI Express 2.0 x16 HDCP Ready CrossFireX Support Video Card - Retail
http://www.newegg.com/Product/Product.aspx?Item=N82E16814150369&cm_re=4770-_-14-150-369-_-Product