Is it my graphics card (ATI Radeon 3450) that's holding back my gaming experience?

Keep in mind the MINIMUM requirements are just that! the bare min. to play the game! the 3450 is quite low for today's games you would be better served with a 5000 series at least a 5770. With that you need at least a 450W PSU (550W would be better) with a 6 pin PCIe connector.