Prim acts like two competing alpha textures

I built a simple gazebo today and the upper step - the part you stand on is acting like it wants to render in front of everything else, like when you have two alpha textures overlapping and the system doesn't know which one is in front. But there are no alpha textures anywhere in the thing. The step is making the columns that rest on it disappear. I thought I had gotten hold of a 32 bit texture, but changing textures didn't help.

I tried unlinking and relinking. I tried rezzing it in a different sim. I even logged out and back in. What am I missing? Do I need to delete and replace the offensive prim and then relink? -- KC

Replaced the offending cylinder - but now the whole structures is showing background trees rendered in front of it or through it.

I can only assume building has had something anatomically improbable happen to it or my graphics card has given up. -- KC

I've run into that too, and only one texture was alpha, the other one was a carpet texture. I don't know why or how to fix it, but I just wanted to let you know that it's not just your graphics card.