There are two problems. First, assignment is denoted by '=', not '=>', which is a glorified comma:

$time{$previous} = {
                           'end_date' => $date,
                           'end_time' => $time
                            };
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Second, in the print statement, you need to dereferene the hash, not the key:

print "$_ $time{$_}{start_date} <br> \n" for (sort keys %time);
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