In theory opengl support is dependent on your drivers - in windows, its bundled into the hardware specific drivers as an installable client driver, and its supported by mesa on linux. OpenGL 2.0 has been out for the past 5 years, so, most semi-modern video cards should support it.
By the speed of the system, i'm assuming its a 2000ish era system, and it predates opengl 2.0. Upgrading the driver MIGHT work (but i doubt it somewhat - drivers for a system that old would be hard to find, and not maintained. ) or a more serious fix would be to find a semi modern PCI based card - unless it has PCI-e and switch to discrete graphics.
With a 56 mb onboard graphics card... modern games are implausible. Even the x3100, which could use a whopping 384 mb of ram (and is about 4-5 years old) can't really handle much outside casual gaming -its on the verge of being able to run source based games (and source scales VERY well) but can't. A video card update should give your system a few more years, IMO