I'd be interested to know if these are games he's always played on the computer and are they online games as well. You stated that you have a Dell Dimemsion 8300 with an NVIDIA 6600 graphics card, by today's standards, most games out there are too advanced for your current hardware set up due to the FPS, anti-aliasing, 3d rendering and such that higher end graphics cards are expected to do in order to perform along side with console game systems.
I can tell you that having an NVIDIA 7300GT I can BARELY play some of the games out on the market now and the ones that absolutely require DirectX10, I can't even load up due to hardware incompatibility.
So before you start unplugging parts and what not, i'd stop and review the MINIMAL hardware requirements of the PC version of the games that he is playing to ensure that the computer is even up to par to run them.
As Bob has stated, unplug the sound card to lower the overall system resources, however, if the hardware doesn't meet the minimum system hardware requirements to even run the game, unpluging the sound card isn't going to make any difference at all anyways.