This could be down to one of two reasons.
Firstly wires could be touching at the rear of the stereo. Cautiously pull the stereo out of it's housing whilst doin so see if the lights go out if so thats your cause. Locate the touching cable insulate it with insulation tabe tis'll stop the lights coming back on.
Secondly it could be a surge was sent during your battery running flat, this may have reversed one of the terminals in the stereo which now sends a positive pulsemaking the light come on.
Cautiously remove the stereo from it's housing when the stereo's out touch the back and if it feels warm / hot it's got a permanent live going trough it.
Synopsis Eventually new stereo.
(X-DJ)
September 2009