Solved! In need of help. Dell laptop black screen problem

[cynicism]

Hey guys, I need help trying to figure out how to resolve the black screen problem on my mom's laptop. I think 2 days ago, when my mom tried to boot up her laptop, the screen just went black and nothing loaded or anything. The lights on the laptop were on, so I knew there was some type of power. We then removed the battery and the adapter, waited 30 seconds or so, and then put everything back and the laptop worked. The next day, the black screen came back and we tried the same method and it worked again.
Unfortunately, this morning the laptop just wouldn't load up at all (the screen is just black) and the take-out-and-reload-battery method is no longer working. I noticed that when I try starting up the laptop, I don't hear the HD nor the fan. The lights are still on though and that's the only way I know there's power.

The laptop is a dell latitude D620 and I believe the video card is a Nvidia. I tried to hook a monitor up but nothing showed up so I am assuming it's a gpu problem. I also read somewhere that there was a problem or something with Nvidia cards that overheated and burned the motherboard or something. Not entirely sure about this.

If anyone can help this would be great. Buying a new laptop right now really isn't the best option but I have a feeling that may be the only solution

 

[house70]

It could be the battery. That one has been depleted many times, is unable to hold a charge. Before buying one, take it to the local hardware store and see if you can test another battery on it. Alternatively, you could borrow a battery from someone who has a similar laptop or at least a laptop with a similar type of battery.
If it were overheating, you should be able to smell something when you are close to it. There is no way that overheating and burning the mobo would not cause a smell.