Well if it din not cause any problems before you got the new ram.Then the problem is in the NEW RAM
Wrong. RAM does not affect any processes that you undertake when running a computer. It provides space for the processes to do what they do. The "M" in RAM stands for "memory".
Most likely this is a problem with the actual game itself. Try re-installing it, clear up any space on your hard drive and shut down all applications and programs before running the game. These applications may disrupt the game's processes and cause it to crash. By shutting down the applications and programs, the game will become less likely to crash randomly.
Try and download the latest Carbon patches. They are basically game updates that fix minor bug and crashing issues. You can find these patches on needforspeed.com and/or various other sites around the net, which you can find by Google.