I am willing to bet that the apartment building is receiving the Dish signal decoding it, and then re-encoding it as a standard def NTSC signal and sending it out over the cable lines on whatever channels they like. This means that you are most likely stuck with standard def, and using an NTSC tuner like you find in a standard VCR. If you try using a QAM tuner you won't get anything extra, and a satellite box will be worthless.
If you want hi-def you are going to need to buy an over the air ATSC tuner box and antenna. You will only get your local channels (if you can get a signal from your antenna).
Again this is my guess, but I believe that is how most hotels, dorms, apartments, etc work.