Well the plus side is simple actually. If you take that PSU and GPU out of that low end computer, and slap it, for example Walmart i5, 8GB DDR3, 500GB+, DVD systems for only $349, you should have a system that can play 1080p High Graphics around 40FPS on BF4 64Man map. Some numbers for the card are listed here with some games but I believe they were tested on a i7 Core http://www.notebookcheck.net/AMD-Radeon-HD-8970M.90656.0.html.
Other examples are : Current 4th Gen i5, $479.99 + $9.99 Shipping
http://www.newegg.com/Product/Product.aspx?SID=5QxxAGs4EeOZD95GYZhP-A0_MIEt3_0_0_0&AID=10440897&PID=1225267&nm_mc=AFC-C8Junction&cm_mmc=AFC-C8Junction-_-cables-_-na-_-na&Item=N82E16883113262&cm_sp=
Or for a little more this awesome deal: i7 4th Gen $599.99 + Free Shipping (Personally this would be a freaken awesome combo for you)
http://slickdeals.net/f/6573552-acer-desktop-pc-intel-core-i7-4770-3-4ghz-12gb-ddr3-1tb-hdd-dvd-burner-card-reader-hdmi-wi-fi-usb-3-0-warranty-windows-8-599-99-ac-free-shipping-w-masterpass-newegg
If your set about AMD CPUs, you can get around the same price but the performance of anything BELOW a FX-8xxx is equal to a i3 Core (entry level CPU), only the FX-8xxx can get up to i5 (mid level and gaming) performance. Nothing still challenges the i7s sadly