Leave apart running....they won't even walk on those specs.......lol..
Get yourself a new gear and spend some time on google...
U dont need to post here coz there is a sureshot list of minimum requirements......(for each and every video game)
Best of luck...!!
a 2.4 core 2 duo will play most games. but your gfx will not. you need a dedicated gfx card a minimimum of which should be no less than a 9800gt or amd 4850 as it will give a 1080p output and minimum settings at the very least on every game that doesnt require a quad core. really though you will need to mover to a minimum of a core 2 quad and a gtx 460 to play all games at above minimum settings on a 1080p screen. just for smoothness sake. as a 460 will give 60 fps on minimum settings on every currently available game. with the option of mid high and ultra on older titles.
you will also want a minimum of 2 gigs of ram if your playing on win7/vista or 8 you can get away with 1.5 but 2 gigs is the recommended minimum now. 4 gigs of ddr2 1066 is perfectly acceptable and is the sweet spot for core 2 quad systems.
currently there is a glut of core 2 firstname.lastname@example.org or better on ebay for £50 some second hand some new. just stay clear of the Q8200 or any other model that has a fixed multiplyer (read the specs b4 you buy) all in you can move to low mid level gaming for about £200 if your current board and psu are good enough.
Best way to go is try a programme like onlive, you can purchase games for a low price or try trials etc and they can run on about any pc, for example I got a really low spec laptop, lower than yours but I can still run games such as Assassin's creed brotherhood, Saints Row the third and any game on the application and there are tons to choose from. Hope I helped.