Several years ago, my sister's HP Pavillion dv2000 series laptop died after about a year and a half. No video. Naturally, she brought it to me as I did spend my early 20's reparing laptops and the like. A quick search turned up dozens of other people experiencing the same exact symptoms with their dv2000 laptops just after one year. Of course the manufacturer warranty is only for one year. What few good mother boards were available were insanely expensive. I advised her to cut her losses and move on.
I found this old HP laptop in my closet the other day. I had intended to donate it to Free Geek for parts. But, I happen to be in the market for a cheap laptop. Another search and I find out fellow geeks on the interwebs have determined the issue is with the video chip overheating. Reflowing the BGA chip often solves the problem. I figured it was worth a shot.
After taking out the motherboard and removing all parts (and disconnecting the CMOS battery), I built a heat sheild. I used a beer can wrapped in several layers of Foil Tape on both sides. I cut a 1" square hole (the size of the nVidia chip) and layed it on top of the motherboard. The idea is to heat up the chip without heating up or melting the surrounding components. Then I used a heat gun (low air flow, hot temperature) to heat up the chip. I kept heating it up until the solder on the components on the top of the chip just started to glisten.
After the first round... viola! It works. To prevent the problem from happening again (hopefully), I put some Arctic Silver Thermal Compound on both the CPU and the video chip before reinstalling the heatsink.