There might be a short (from a trace or from some silicon failing) or the regulator might have failed and is the short itself. If you can replace the regulator, it's worth a try.
If it's a short somewhere else...that's a massive pain to find and if it happened inside an IC you are pretty much outta luck.
Do you measure a low resistance between power and ground (on either the input side of the regulator or the output side of the regulator?). How about when you connect power? Do you measure zero volts between power and ground (on either the input side of the regulator or the output side of the regulator?)