2-dimensional Date Range Criteria

Attached is a really simplified version of what I'm trying to accomplish. I'll attempt to get my brain working well enough to explain it:

For each row, I have a person's name, their department, their site, and then a series of dates (representing dates of attendence). The four columns after the dates ("Counts" is the first) are me trying to keep all the right numbers in mind, and are the routes I've been trying to take on this. I have also tried to make a custom formula called ClassInRange, which isn't playing nicely.

What I eventually need to populate is the little 2x3 section at the bottom where the three sites and the two departments I'm working with (down from 5 sites and 8 departments for the sake of sanity). What I need to be able to do is populate those cells with something that will tell me how many people from which site and department have attended something within the date range.

So, for example, I need to know that the 2 guys in Wellesley attended something between January 1st and December 31st of 2007. (American date style, in case anyone's lost)

If you're able to help, please keep in mind that I'm not the end-user; I'm just the slightly crazy dude trying to create this thing and make it simple to use. Eventually, the Dept/Site box will be part of a template which is copied and pasted up to four times on a report sheet, each fed by different date-range criteria.

Also, the important information is the person's name, dept and site, which I hope gives some reason behind the organization; we want to find the person easily.