Are you sure your laptop has 2 hdds or is it a single hdd that is partitioned into 2? Very few laptops have 2 physical drives but some do so just want to make sure.
What exactly do you mean when you say that one drive appears to be broken? Are you able to access it at all? If it's not accessible then it may not be possible to get the data from it. Depending on why it's not accessible, it may be possible to attach the drive to another computer and copy the data from it.