This seems to work:

use Modern::Perl;

while (<DATA>) {
    chomp;
    do { say "Not a valid file, Check output!";    next } if /[^0-9A-F
+]/;
    do { say "All zeroes or empty, Check output!"; next } if /^0*$/;
    say '==', join "\n==", /(..)/g;
}

__DATA__
00000FFEDFF67FFB8FF96FFE200BBFF240020FFBAFF360132FF6500FCFED30079
000000000000000000000000000000000

THIS IS NOT A HEX DUMP
[download]

Output:

==00
==00
==0F
==FE
==DF
==F6
...(snip)...
==0F
==CF
==ED
==30
==07
All zeroes or empty, Check output!
All zeroes or empty, Check output!
Not a valid file, Check output!
[download]