Short answer: This is a convenience sample. There is nothing you can do to justify it.
A somewhat longer answer: you are in the same boat as many social networks that run their internal surveys without having much idea as to who would respond to a one-question survey that would appear randomly on Facebook or Google+... except that unlike these giants, you don't have any data on those who did not respond. The survey and public opinion research community generally frown upon this type of work, as it is not at all clear how the results of these heavily biased sample can be generalized to the total population (if at all). You can attempt to reweight according to the known demographics, but then you will end up with a variation of weights from 1 for a person who only represent themselves to 1,000,000 assigned to the only 70+ male in the population who knows how to use a computer (and is likely not representative of the remaining 1,000,000 70+ males, anyway).
Additional reading: "How To Lie With Statistics" opens with a chapter on biased samples. If you can read it and not weep in frustration about your sample design, you can move on. If you rely on volunteers, your sample with be biased towards young and urban populations with better access to electronic gadgets. Likewise, "What is a Survey" booklet put together by Fritz Scheuren, past president of the American Statistical Association, opens up with the picture of Harry Truman whose victory could not have been predicted by the biased polling techniques that existed at the time.
There is some research on hard to reach populations. One well-known project was a study into the number of excess deaths in Iraq where geographical areas were sampled, and in each area, the local doctor would try to solicit interviews from every household in the city block. There's been mounting critique of this design, but however compromising it was, it still had its sampling component. See papers in Lancet (as you probably know, you cannot get any more prestigious in the medical world) http://dx.doi.org/10.1016/S0140-6736(04)17441-2 and http://dx.doi.org/10.1016/S0140-6736(06)69491-9.