While it is possible to implement some Turing-equivalent systems (such as Rule 110 - http://eli.fox-epste.in/rule110-full.html) in HTML and CSS alone, the resulting implementation cannot be used as a computer in any useful sense. It has an extremely high overhead, and would take an absolutely gigantic web page to perform even very simple computations (e.g, adding together small numbers) with. A Java compiler would be utterly impossible.
Take-home lesson here: Not all "Turing-complete" systems are equal. There are vast differences in how efficiently they can get work done.