Are the doorbell xfmr and the ceiling fan on the same circuit? I'm wondering if there's a box where these circuits meet someplace and they accidentally were crossed?
How old is the TV? Could it have a capacitor that's "kinda" working but on the weak side?
Are there any dimmer switches that the fan and/or TV outlet might be tied into?
Have other motor loads been tried on the same circuit as the TV? (Plug a vacuum cleaner into the TV duplex and see if the same issue occurs?)
Cheap ceiling fans tend to be *noisy* when run off of external fan controllers at lower speeds (The kind that hide in the ceiling fan canopy.) but the doorbell is throwing off my theories....
