Roger -
The 110V line could well be causing interference if they are running parallel for that distance. A good rule of thumb for separation would be to keep them 8 ~ 12 inches apart at minimum if possible. (Crossing a high power line at right angles does not affect you as much as running parallel) If the camera is 3 years old and this problem has just started - the camera itself may be producing a weaker signal now, and just starting to allow the interference to affect it. (All electronics degrade over time with use) If possible - see if you can get some more separation in that 15~20 foot run. That may be our culprit.
As for the 12VDC line burning the cable in half - I am guessing it was siamese cable (coax with the 12 volt lines attached as a seperate cable) Did that burn through the coax as well, or just the 12VDC part? I have been in this industry for 14 years now and have never heard of that happening. Usually the 12VDC is fused or has thermal breakers in the supply side that should have killed the connection before it gets that hot. (referring to a 12VDC power box where all cameras connect to same power supply) If you were using 'wall warts' they may not have that same protection though. Rest assured that is a pretty rare occurence for a 12VDC line in any case.