Trying to figure out how this service panel is getting electricity
You will just need to shut off breakers to isolate each wire and check it for voltage.

Turn the main breaker off, and check the incoming lugs for voltage.  If present, then the power has not been "shut off".  With the breaker still off, check the lugs that attach to the sliver bars in the back of the panel.  

If there is voltage on the bars, one of the breakers is "back feeding" voltage.  Turn the breakers off one at a time to see which breaker it is coming from.