Rat brings up a VERY good point, what I would recommend, get a volt meter, and plut it into some of the outlets on the surge protector that your projector is pluged into.. play a dvd, and watch the voltage, and try to watch the movie, or have a buddy watch the picture, while you are monitoring the volt meter, and when you get to a sceen with bass, monitor the picture to see the problem you stated, and also monitor the voltage, if the bass comes in picture goes to crap, and there is a drop in voltage then your problem is the amount of current hat your sub is pulling from the breaker.. and a line conditioner will solve this problem, but that is a very expensive way to solve the problem, one simple way to fix the problem is to plug the sub into an outlet on one breaker, and the projector into an outlet on another breaker. The rute cause is the wireing in your basement the wire is to small of gage of wire for the amount of current you are trying to draw; so when your sub starts making the noise, the sub amp is wanting to draw a lot of current, and when the amp wants a lot of current the line voltage will drop if the gage of wire is small enough due to I squared R losses.
Sure you can spend 200$ on a line conditioner; but that is just a fasad not a real fix to the problem, you will have a hard time, if you decide to get bigger amps for your main speakers, or add more eletrical stuff in your HT room.
Your projector power supply is probably much more sensitive to volage changes than your tv ever was..
