The majority of laptops, especially old models, have onboard graphics. In this case you can do nothing if the chip fails - it's soldered to the motherboard. New motherboard required. If your laptop has a separate graphics card, it can be replaced.
The problem is that you don't know for sure that the graphics card is at fault. Laptops have a variety of power saving and resuming features that may blank the display if they go wrong (which is why I suggested pressing the reset). You can't run any diagnostics either if there is no visual indication.
Assuming your laptop has a separate graphics card, if you are going to replace the card yourself, check the return policy of wherever you buy it. If the card is not the problem, you want to be able to return it. Alternatively, take the laptop to a dealer for repair - let them deal with new components.
Depending on the laptop model, you may find an online guide for dismantling. Often there is a trick with what to pull apart first.
Starman*