How to measure or estimate the prevalence of psychopathology in a particular school? I wrote a research paper regarding the mental health of adolescents at a local magnet school, emphasizing the sources and affects of stress and the subsequent vulnerabilities it poses to developing forms psychopathology. 

My problem: I need to formally establish that many students struggle with mental health problems. My initial idea was administering the BDI but, long story short, it can't happen. How else should I go about "formalizing" statistically the prevalence of psychopathology among the student body?
The answer to this question depends on your ultimate goal. If you want to know whether or not students at this school are more likely to suffer from a psychopathology/s, you'll need to compare them to some other population. This other normative population can be students at another school, students in the country, students in the world etc. If you don't have access to data on another population you won't be able to use most of the truly inferential statisticsal procedures. 

If you want to look at the school in isolation, you can use descriptive statistics and "describe" the situation at the school by looking at the way in which psychopathologies present, or, are distributed at this school. Additionally, you can have some arbitrary cut-point or score that you can use to make a judgment call. This probably won't cut it in an academic journal though, depending on the journal and field. 

Reiterating Russell's suggestion, you can look at the correlation between the incidence of psychopathology and these stress factors you mentioned. This will at least allow you to compare these students to a hypothetical population of students where there is no correlation between psychopathology and these stress factors.

Your starting point will likely be to properly operationise your variables and then scouring the literature to see if you can glean something to compare or even make sense of your data from it.

First prize will be using an established and validated instrument. If you can't, you can still try and wing it, but be careful of the interviews though. To use the type of statistics I think you're hinting at, you need to properly operationilse your variables and quantify them. This is going to be hard to do with open ended questions, for example.