Perl, 172 characters
Perl, 333 251 203 197 190 172 characters. In this version, we randomly push buttons until all of the lights are out.
map{$N++;$E+=/\*/*1<<$t++for/./g}<>;
$C^=$b=1<<($%=rand$t),
$E^=$b|$b>>$N|($%<$t-$N)*$b<<$N|($%%$N&&$b/2)|(++$%%$N&&$b*2)while$E;
die map{('.',X)[1&$C>>$_-1],$_%$N?"":$/}1..$t
