MacBook Screen/Graphics Issue?

Hi, my mom has a MacBook that is starting to show its age I think. I think it's the first model. The specs are a 1.83 GHz Intel Core Duo, 1 GB RAM, 60 GB HD. I believe its optical drive and battery have been replaced through Applecare. I have noticed after restarts and after some wake-ups that the screen brightness flickers. It seems like full brightness to a bit under to full again and keeps doing that for some time. Any ideas? I am a bit worried because I think the graphics card is failing.