If there is an image on an external monitor, the display is likely the faulty part. If there's no image on an external monitor or the internal one, it's the mainboard.
Welcome to the Community.
If it were the main board the problem is with the graphics card. As the graphics cards is integrated on the system board you will need to replace the mother board.
If the system was purchased in USA and is under warranty you can click on my user name and add me as a friend and send a direct message with the service tag, name and contact number so that I can help you set up a service call. However if the laptop is out of warranty, please contact Dell Out of Warranty Repair on : 1-800-288-4410
Glad to help.
If reseating the memory doesn't fix the problem, it could be any one of a host of things - none of which are repairable short of a mainboard replacement. Whether you want to spend at least a couple of hundred dollars on a system that's four years old is up to you - from an economic standpoint, you're probably better off taking that money and putting it toward a new system. After three years, any notebook is on borrowed time.
If an external monitor doesn't work, it's a GPU issue.
Nvidia produced 8600M and 8400M chips that were ALL defective in the 2007- approx 2010 year. They ALL used a material that basically melted under high temperatures. They attempted to cover it up, but end users from Dell to HP to Apple reported extremely high incidents of GPU failure. This lead to a no-fault settlement deal that has already ended in 2011.
This is like buying a car faulty transmission that will inherently go bad. Dell updated their BIOS in revision A08 to lower the system fan temperature threshold lowering battery life, but increasing noise and and the time it would take for the GPU to fail due to overheating.
Dell has agreed to provide a 1 year extension warranty to a maximum of 5 years total warranty. So if you had 4 years warranty, you now have a 1 year extension. However, that one year is only for this specific GPU issue.
In this situation, they will replace the motherboard as the m1530 GPU is soldered onto the motherboard and the entire thing gets replaced for FREE by Dell.
If you are out of warranty for 1+ years, then you might be screwed. You can try Tech support and ask for a free repair due to the inherent nature of the faulty GPU. Try with at least 5 calls. If that doesn't work try contacting their corporate headquarters or social media accounts.
The continuing problem here is that even if it replaced, no one can guarantee the new GPU will not fail in the future as no one can confirm if a new GPU with a correct material was used or if the correct material works. There have been reports of replaced GPUs failing, too.
Your best bet is to buy another computer.