Try this. Download the latest graphics drivers for your motherboard from the manufacturer. Uninstall the existing drivers (using Control Panel -> Programs and reboot. Windows may restart in safe mode otherwise in a low resolution display mode. Install the latest drivers you've just downloaded. Reboot at the end and try to run your OpenGL games again.
Note that the G41 chipset supports OpenGL 2.0 but this should be backward compatible. Your game doesn't require OpenGL 3.0 compatible hardware does it?