You know, call me crazy or whatever, but it seems kind of backward that video cards these days have no redundancy in their cooling system!  Granted, there may not be many places on a video card that you could fit an extra fan and still have it work, but it would be a nice idea if one of the card makers actually addressed the issue instead of making cards as cheaply as they can to melt as fast as possible.

Lord how I hate those little cheapass cooling fans.  I found a nice fanless video card for my wife's computer and it works well for the games she plays, has a giant heat sink, but that's not a problem since the box has no other peripheral cards.  My computer has a big card with a good fan so that's not a problem.  But, yea, I go out of my way to avoid those kinds of fans, but with a laptop, it's not much of an option. 

I'd go ahead and replace the card.  I had a video card that burned out, did the same kind of thing, ended up replacing it.  Even if it's only a cooling problem, the chip is probably shot from overheating anyway.  Those damn video chips run so hot anyway, I find it amazing they last as long as they do.

You should probably read the topic title again... 

Laptops are all different.  My laptop has the fan on the card so I assumed incorrectly.  Either way, I'd replace both the fan and card.  At least try to find a fan with a dual ball or other high duty bearing.  Those crappy little fans almost always use sleve bearings that don't last very long.