At this point in time, $500 will get you nowhere, your choices as far as i can see are:
1) You save up your money for a computer rig that will run BF4.
2) You buy a new console as suggest by jb6684.
3) If you want a computer and not a console and cannot save money, then i suggest going on sites such as Gumtree and find good deals, make sure that you see with your own eyes that the components are in working order with a stress test before purchasing second hand goods.