This computer sounds like it has the same problem as every other DV series laptop and that is the fact that if they overheat in the slight bit, the solder on the Nvidia chip hits its de-solder point and the chip looses contact with the motherboard and causes all kinds of issues. I have "reflowed" dozens of these motherboards and have a 90% success rate and getting them to run again. If you have a heat gun, I can walk you through the steps to reflowing the board. You have to understand though that it may work and again it may not. In the times when I have not been successfull, I simply replaced the motherboard.
Take the laptop apart, I'll give you a link below for the service manual that explains the process.
The Nvidia chip sits next to the processor chip, wrap the motherboard in aluminum foil to ptotect all the areas except for the top and bottom of the affected chip.
Now, clamp the motherboard to a desk so it will not move and make sure that the underside of the chip is accessable from underneath.
Get a quarter and wad up a small amount of solder and place it on the quarter. Now put a small amount of thermal paste on the chip and place the quarter on the chip with the solder up. (The solder will be the indication to you that the chip has reached the proper temperature to melt the solder on the chip).
Now, take the heat gun and on the first heat setting start heating the top of the chip for 30 seconds, then switch the gun to the bottom of the chip for 30 seconds, then go back to the top for 30 seconds and then to the bottom for 30 seconds.....now, switch the gun to high and hold it to the top of the chip where it will blow down on the quarter, keep the gun at least 6 inches away from the board at all times. When you see the solder on the quarter melt into a drop, switch the gun to the low heat setting and put the gun about 12 inches away and sweep the gun from side to side or have a ceiling fan over the area and let it blow air softly down on the board to help gradually cool it. Do not bump, hit or disturb the board until the board has at least 30 minutes to cool down. Once the board cools down, remove the quarter and reassemble the laptop. Power the ****** up and see if it fires up. Below is the link to the service manual, copy and paste it to your web browser address bar. It is in a PDF format and is free to use, copy and print.