Two ways come to mind:

1) Preformat your variables correctly:

1a)

$day    = sprintf('%2d',  $DAY);
$hour   = sprintf('%02d', $HOUR);
$minute = sprintf('%02d', $MINUTE);

print("<b>$1</b> $2\n", br)
  if m/^(... $MONTH $day $hour:$minute:.. .{4}) (.*)/;
[download]

1b)

#                      Thu Apr  7  03 : 00 :39 2005 
$time_stamp = sprintf('... %s %2d %02d:%02d:.. ....',
   $MONTH,
   $DAY,
   $HOUR,
   $MNUTE,
);

print("<b>$1</b> $2\n", br)
  if m/^($time_stamp) (.*)/;
[download]

2) Extract the parts and compare those:

print("<b>$1</b> $6\n", br)
#        Thu  Apr    7   03 : 00 :39 2005 
  if m/^(... (...) (..) (..):(..):.. ....) (.*)/
  && $2 eq $MONTH
  && $3 == $DAY
  && $4 == $HOUR
  && $5 == $MINUTE;
[download]

I prefer #2