I can see two problems. Change:

my $foo = MyModule::->new($dbh);
[download]

unless that's just a typo, into

my $foo = MyModule->new($dbh);
[download]

Also as was mentioned previously, you probably want to change your new function to start like:

sub new
{
    my $class = shift;
    my $self = {};          # self is a hashref.
    bless $self, $class;
....
}
[download]

because the very first thing your new function gets passed when you call it as MyModule->new(), is a scalar containing the string "MyModule". You can bless that scalar into any class you might like, but you can't magically make it turn into a hashref. Without reassigning it anyway.