SiS is far from a no-name brand, so I wouldn't expect an actual dodgy card based on that alone. With that said, graphics cards are far from their main niche so it's possible it's just not too well optimised for a lot of games and is better suited to more business-like graphics card use (Windows Vista, Photoshop, etc).
Drivers are pretty much the only thing I can imagine making a significant difference, as well as making sure superfluous effects like anti-aliasing aren't enabled anywhere. If it still runs badly, it might just be a limitation you have to live with.
In future I'd make a note of aiming for an NVIDIA or ATI GPU if possible. While other manufacturers do decent laptop cards and such, they don't aggressively optimise their drivers for each new game that comes out like the big two do. That is also why keeping your drivers completely up to date is vital.