Try this...PCPartPicker part list
/ Price breakdown by merchant
/ BenchmarksCPU: Intel Core i5-3570K 3.4GHz Quad-Core Processor
($189.99 @ Microcenter) CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler
($29.98 @ Amazon) Motherboard: ASRock Z77 Pro4 ATX LGA1155 Motherboard
($98.99 @ Amazon) Memory: G.Skill Ares Series 8GB (2 x 4GB) DDR3-1600 Memory
($44.99 @ Newegg) Video Card: MSI GeForce GTX 670 2GB Video Card
($359.99 @ Newegg) Case: Corsair Vengeance C70 (White) ATX Mid Tower Case
($69.99 @ NCIX US) Power Supply: XFX 550W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply
($53.99 @ NCIX US) Total:
$847.92(Prices include shipping, taxes, and discounts when available.)(Generated by PCPartPicker 2012-12-26 23:51 EST-0500)
It'll have all the power you need to play Battlefield 3. If you need an optical drive, just reuse the one from your gf's old PC. If you don't have one, then just get a cheap lite on.
I also highly recommend you at least get an overclockable CPU so you have the option. You may change your mind once you've had time to research it a bit more.
If you have any questions, feel free to ask.