Is it needed to have graphic card to run games on PC

I have a problem with my PC. No game runs on my PC. Mines was a 10 year old specimen(although till 2004 almost all games use to run in my PC). Recently I upgrade my SU. Present configuration is given below:
Intel Core2Duo 2.8 GHz processor
2 GB DDR2 RAM
320 GB HDD.
I dont have a graphic card in my PC. Now I find that no game runs on my PC although I can install them. Strangely I find that the games which use to run on my PC earlier, they also dont run now. I guess for the latest games I may need a Graphic card but games like Project IGI etc which uset to run on my PC earlier than the upgrade also dont run now. I have a better H/W now but still games dont run Surprisingly I find the games like Project IGI2,EA Cricker 2005, GTA Vice City etc runs on my pal's PC who has a simillar H/W as mine



Pls tell me what should I do to have games runs in my PC(atleast those which use to run earlier).