my $line='';
while (<INPUT>) {

  # build line
  chomp;
  if (/^(.*)\\$/) {    
     $line .= $1;  #or maybe $line .= "$1 "; ???
     next;
  }
  $line .= $_;

  # ... do line processing here ...
  if ($line =~ /^Data_Value/) { ... 
  } elsif ($line =~ /^Data_Group/) { ...
  } elsif ($line =~ /^Data_Raw/) { ...
  }

  # reset state
  $line = '';
}