When I print $data_pair->{'key'} gives me all the keys present in the array
When I print $data_pair->{'values'} gives me all the values for the keys

Your data structure is strange :-)

I think you need something like this:

my ($cor, $date);
for my $data_pair (@data_list) {
  if ($data_pair->{key} eq 'correct') {
    $cor = $data_pair->{value};
  }

  if ($data_pair->{key} eq 'date') {
    $date = $data_pair->{value};
  }
}

$sql_content .= qq(
INSERT IGNORE INTO correct SET
       text="$cor",
       date="$date");
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But as others have already mentioned, using DBI placeholders makes far more sense here.

my %h = (
   correct => $some_value,
   date    => $other_value,
   ...
);

# later on you can retrieve the data like this, without any iteration:

my $date = $h{'date'};
my $cor  = $h{'correct'};
[download]

Learn about hashes, they are really worth your time.