Whenever a cell phone rings near my Insignia NS-LCD32 the sound goes away and the picture gets static-y. This did not happen when I was at my old apartment...it just started happening when I moved into my...
This is a common problem for a lot of electronics these days: unwanted interference from a communications device. It is usually caused by a lack of proper shielding inside of the unit to absorb and redirect stray electromagnetic signals. But If it has started since you moved, then I suggest checking the outlets as a start.
Is the outlet 2 or 3-prong? If it is 2 prong, then that is immediately the problem. The electrical outlets should be 3-prong, with the round hole being the ground. If the wiring in the building is old 2 wire, but the outlet is 3-prong, the outlet's ground hole is not hooked up to anything, therefore, cannot carry the interference away from the TV.
There is a possibility that the wiring may be reversed, as well, which does cause all kinds of problems.
You can purchase an outlet checker from any hardware store, and they are always a great thing to have in any case. Check every unknown outlet for problems, and it may save your equipment, and you, from damage/death in the future.
If your outlets are the culprit, then a GFI (ground fault interrupter) outlet can be safely installed, and usually works fine (it compares the neutral and ground current, and makes a connection in the process).
Give this a shot. Post your findings if you would like.