I looked at your code, deleted the comments and with an adjustment of whitespace we have this:

my @seqnames;
my @sequences;
foreach $line(@DNA)
{ 
   if ($line =~ /^>/)
   {
      push(@seqnames, $line);
   }
   else 
   {
      push(@sequences, $line);
   }
}
[download]

Its hard for me to see how both arrays could wind up being "blank" (no entries).

Perhaps this is what you want, but I'm not sure:

my @seqnames;
foreach $line(@DNA)
{
   if ($line =~ /^>(\w+)\s/)                                
   {
      push(@seqnames, $1);
   }
}
[download]