Sorry to hear that, though the dropping on concrete circumstances sound odd in itself.
You should take the Hard Drive to a tech specialist, there should be some in your area. In most cases, the Hard Disk itself is in tact unless the physical disks were damaged. If it was a SSD drive, then chances are it survived the fall (unless the casing or physical chip is compromised.) As long as you can hook up a SATA cable and some form of power (without frying the drive), you should be able to pull the data off of it, unless the drive itself is hosed.
On the positive side, this can only mean you will receive a better, more powerful system at some point in the future (if not today, then maybe next week, or next month, or next year.)
This also shows the extreme value of having virtual and/or physical backups of your important data at all times. I recently purchased my sixth external drive to house redundant backups of all of my data simply for worst case scenarios such as this. Now I hardly expect you to run out and buy $3500 worth of drives, but a good place to start would be one of the
$60 external Western Digital
drives. I use a free software known as
SyncBack
to automatically mirror my data onto my backup drives so, at any time, if my computer were to unexpectedly fail, I still have all of my precious data.
Hope all works out for you in the end. Remember to have your primary drive looked over, it's possible the data is recoverable so long as there is no physical damage to the drive itself!
~Aayrl
My dedicated Marble Blast computer has died completely.
Or I will, when the six hours is up from increasing someone else's karma. 
