sub new {
    my $class = shift;
    my $self  = {};

# Get message strings from subroutine call
$msg  = shift; # message text
$app  = shift; # application label
$obj  = shift; # object
$sev  = shift; # severity of message 
$msgg = shift; # message group
$ser  = shift; # service id

    return bless $self, $class; 
}
[download]

The data still goes missing.

Given the use strict that code won't compile, so one presumes that you still have my $msg = shift; etc. That means that those variables are scoped to the new sub and disappear after it returns. You want to store the values off in your instance and then retrieve them from there later.

package Foo;

sub new {
  my $class = shift;
  my %self = @_;

  return bless \%self, $class;
}

sub do_something {
  my $self = shift;

  print "msg is: ", $self->{msg}, "\n";
}

## Meanwhile, back on the ranch . . . erm, in the main package
package main;

my $foo = Foo->new( msg => "WUBBA WUBBA" );

$foo->do-something;
[download]

Those scalars drop out of scope and are lost. You should store the values in the $self hashref ... as the example I referenced previously shows.