The laptop has an integrated nVidia Go 6150 chipset on their RV309UAR systemboard.
If your diagnosis is correct an the graphics chipset has failed, then it's not really possible to identify where on the board thet has happened. It might be one of the chips themselves or simply a solder joint or capacitor that has broken. As the grphics components are not modular it would mean unsoldering them and reattaching another identical component and even getting that done is such a precise task that it's likely most people would make things worse. It's also possible that the failure of one component has cause other parts of the system to fail too, particularly if this has been going on for a long time.
So it's possible to do what you are asking but the likelihood of success and the time taken would be outweighed by the price of either a replacement board or even a new laptop (as new systemboards are often around two-thirds the cost of the as new price of a laptop).
