Can I run a game on old CPU socket 478 2.4GHz with new video card with 512M DDR2 without any problem i.e the game will run fast as well

It depends heavily on what your playing in all accounts. If your playing anything equal or Above the graphics of World of Warcraft, then I suggested getting more Memory. Most games now a days wont run max settings with out at least a dual core processor as well as at least 2GB of RAM. But I personally run Aion Online with a Single core 2.4Ghz processor with only 1.5GB of DDR RAM. I'm at max Settings and I run about 20 Frames per second out side busy areas. So all I do is just move my settings down one notch and it runs smoothly. Hope this answered your question.