All of the laptops that I have seen fail failed as a result of the video card; the display becomes corrupt and starts working intermittently, and then doesn't work at all.
My Dell Inspiron 8500 (2003, GeForce4 4200 Go) lasted almost 7 years and several drops and spilling water on the keyboard while powered until the video card died recently. I left it on for hours working with MiniDV video and encoding to DVD for media projects, playing games (BF1942, CSS, other 2000-2005 games), and watching movies so I'd say 7 years is an impressive achievement.
My Acer tablet (2003) was fine for about 4 years and then I lived with a garbled display until I sold it in 2009.
My friends' Acer with a Radeon x#00 lasted only about 2-3 years before the card died; I sold the parts. Another's Inspiron 6000 lasted about 4-5 years before his Radeon x#00 did the same thing.
I think dedicated video cards are a big factor in failing laptops. I'm hoping my two Dell Latitude D630s will last longer with integrated graphics; they're both about 2-3 years old now.