Ive got nfs the run and im running it on a i7 2600, 16gb, ssd and a hd4850 gfx card and sometimes it seems to be really laggy when cops chase me etc, ive got all the graphics textures set to low and vsync off, atm im running it on res 1680 by 1024
The only thing I see there that is even somewhat questionable is the video card. The 4850 was a terrific card in its day but a little bit out of date these days. Check your game specs and see what is the minimum versus the recommended gpu for that game. Maybe THIS will help you determine how your card ranks with the game's requirements.
The other things you could look at are:
the PSU size and connections to the video card (if any)
whether or not your running a lot of stuff (software) in the background while trying to play the game. you should turn everything off except for the bare minimum (read that as anti virus/anti malware/ internet security only)