How about this?

   Offending code removed
[download]

Clearing the record separator ($/) makes it take the entire contents of the file on read, this also preserves the new line chars, though, too.

HTH

Update:tilly's right on the mark: an answer using proper code takes precidence over minimally changing the presented code to work. So, this is my final answer, ie., how I would've done this from scratch:

my @member_list = qw( fileone filetwo filethree ) ;
my @all_members = () ;
for my $file ( @member_list ) {
   open IN, "$file.dat" or die "Can't open '$file': $!" ;
   local $/ ;
   push @all_members, <IN> ;
   close IN ;
}
[download]

-Ducky