Technically, yes as the other posted, however I would question your definition of good processor.
The thing is that igp with shader 4.0 started being common in 2007 (because of vista), unless you took a gpu from an older computer when building yours ( explaining how you can get shader 3.0 + good cpu) , I'm afraid your cpu may be barely capable enough to play some games from this year.
If you look at the thread "bf3 input lag" (http://gbatemp.net/topic/312732-battlefield-3-input-lag/), the guy has a cpu that seems to be about that old and he can't get decent performances in bf3