Yeah basically that seems to look like a cheap graphics chip just built in to the motherboard to basically get something on your screen, and it's pretty old too. I doubt the makers had any interest in supporting DirectX. I couldn't even find much in the way of specs/features, except an ATI page with marketing fluff, and the drivers are hard to come by too. The drivers are pretty old - 2004 according to your details - maybe there are newer ones? Try looking for drivers for your laptop model, or motherboard model if you know it. I found official drivers for Windows 2000, but not XP! Lousy support huh? Unfortunately if none of this works, I think you just need a new computer... Construct uses DirectX 9, and if your computer doesn't support it, that's it.
I guess your PC just can't run Construct because it's too old, but it's slightly possible I coded a subtle bug which has broken it just for your very old chipset. But that's pretty hard for me to test.
We may write a software renderer in future which would work but... not any time soon I'm afraid!