It's a simple case of re-factoring to strip out this redundancy. Make a simple template function first:

sub getById
{
     my ($table, $column, $id) = @_;
     my $dbh = sqlConnect();
     my $sth = $dbh->prepare("SELECT * FROM $table WHERE $column=?");
     $sth->execute($id);
     my $result = $sth->fetchrow_hashref();
     $sth->finish();
     return $result;
}
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Now you can call this function with the appropriate parameters, or, try and make these wrapper functions:

sub getCustomerById
{
     my ($id) = @_;
     return getById("customers", "cust_id", $id);
}
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This can be tuned to match any of your various "getXById" functions by simply supplying different parameters.