Well, put on your thinking cap, this gets a bit involved

I take it it's impossible to get another line into that room.
You can share one cable to carry both "cable" TV and Satellite signal (the line between the dish and receiver) by using a pair of parts called "diplexers". The problem is that the model receiver you have, the 625, is a twin tuner/2 room model and it needs that line to also send information to TV2, usually on channel 73.
Through a real mess of splitters & diplexers you could hook it up to accomplish what your trying to do but you are then sending channel 73 (or whatever chan you set) back up the line to your cable company and even if they don't notice it and complain it usually doesn't work anyway, the cable signal tends to swamp the TV2 output signal from the Dish rec.
If you stopped using the TV2 portion of the 625 and only used it for the basement TV, it would work. You would also get better DVR functionality and PIP right from the 625.
Good Luck,
Brad