You CAN upgrade from 802.11g to 802.11n but I can almost give you a certain answer that it will do NOTHING to effect your internet speed. Internet speed is GENERALLY less than 10 Meg, while WIRED LAN is 100 - 1000 Meg, depending on your hardware.
Out of curiousity, how do these SAME games play in single player... I would suspect most of your trouble might be with the ATi 9200 video card. I rebuilt a PC for someone recently that had a 9250, and it could barely run The Sims 2.