Replace motherboard for better graphics?

Laptop motherboards are usually not upgradeable. The only companies who make boards for them is the original manufacturer of the laptop, and the only time they would supply you a motherboard is to replace one that failed. There is no standard form factor for laptops as they are all a little bit different in design from one manufacturer to the next. I suggest upgrading the memory and possibly hard drive on this laptop as much as you can to improve the performance, or just save up for a new one.
Another option, you can connect the laptop to an external monitor if you have any and check if here is any difference.

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