Diagonal Non-drawn line through textures

Developing my opengl program on an Nvidia 8600, I get no problem, but then when I test it on either an Geforce 4 Ti, or Intel integrated graphics (I don’t have the exact model, but I could get it if required), I get a diagonal (non-drawn) line through my textures top-right to bottom-left. How can I avoid this?

Debian machine with 8600, and two Ubuntu Hardy with the Geforce4Ti and Intel graphics.

I am uning GL_QUADS at the moment, but the result is the same using GL_POLYGON, and I am using a POT texture (256*256 pixels).