http://stackoverflow.com/questions/2497146/is-css-turing-com...
where the top answer gives a Rule 110 solution, but I was satisfied with this comment:
"BRILLIANT!. However, I don't think this qualifies as turing complete. CSS is only able to calculate 1 iteration of the state-machine. Your example relies on the human repeatedly clicking all the orange boxes in order to feed the "output" (pixels) back into the input (page state) and "pump" the state machine. Because there is no programmatic way to use the output of CSS as input, it can't be used to calculate any multi-step loops, the hallmark of turing-complete languages."
See this: http://www.turing.org.uk/turing/scrapbook/tmjava.html
But CSS is required for the site to look right There's no way to turn it off without messing with the site's layout.