I've used PCA, but I'm no expert, and I have no knowledge about accounting for missing data. But clearly from Fabrice Clerot's response, others have addressed the problem, so I'm sure you will find the answer. My first thought is that if I were faced with that problem I would look for the strongest binary correlations/regressions between pairs of variables, excluding the missing character/structure, and estimate its value from them. The only text-book I have, Harris's "A Primer of Multivariate Statistics," doesn't seem to address the problem, but mine is not the latest addition.
The freeware PAST (http://folk.uio.no/ohammer/past/) offers two methods to account for missing values (see manual). Moreover, the software is very easy to use.