I don't think it'd be a waste of money to upgrade your rig with a graphics card. The AMD Athlon II x4 was introduced in mid 2011, so it's only a little over a year old. Personally, I'd also upgrade the CPU cooler, or at the very least replace the thermal compound since HP probably went with a low quality compound that may make things difficult for the processor sooner than they should. You'll just want to make sure your power supply has the connections necessary to power whatever graphics card you choose.
Edit: You may also want to check HP's policy on user-upgrades and how that may affect the warranty (if you still have one). I'm not sure if HP is one of those companies that will void your warranty for adding a graphics card.