Thanks to you both, Dani and RD, for your advice!
RD - It was much more informal than a normal housing arrangement because the homeowner used my seminary to find a tenant. In general, people who use the seminary have an extra room or a basement to rent out and they want a Christian grad student to live there because (I guess) they figure we're honest and quiet. I've never heard of anyone having such crazy issues with the homeowners in this area. I live in "metro" NYC and the housing around here is ridiculous. The rent for this particular basement included all utilities, so rent is a bit higher for such a small space.
I can't find even a small studio around here for less than $900 (before utilities).

It's really awful! Everything under $900 is in a private home.
I have an update... my fiance called the homeowner from his own phone and she finally picked up. I have found out the she wasn't planning on refunding the money because I had "inconvenienced" her. But, surprise surprise, she
already has a new tenant in the wings!!!
BTW - I just called one of my witnesses today to reconfirm, one more time, that I wasn't just remembering what I wanted to remember and she said that the homeowner DEFINITELY stated that she would have the tenant immediately begin looking for housing (back in May) and that the intended deadline would be the beginning of September. So, basically, the homeowner is all out lying.
P.S. The apartment takes up only a portion of the basement and tenants do not have use of any other part of the house. The rest of the basement is sectioned off and is used by the family for storage and laundry. AND, the apartment tenants DO NOT have use of the laundry room. Ain't that foul! LOL! But, it wasn't a problem for me at the time because I know that washers/dryers are very expensive to fix if anything goes wrong. I truly am a reasonable person.
Oh and, no, I didn't check to see if the basement was to code. The thing is, it is SO hard to find rental properties around here that you really have to take whatever you can find. Anyway, this type of arrangement is set up all the time for the seminary grad students so I really was hoping for the best. That was simply foolish on my part. Never again!