The short answer to your question is: No, the recovery disk will not work.
The long answer is: Given a few steps, you may be able to use the recovery disk to restore certain settings.
First and foremost, get into the BIOS and do some Hardware testing to see if the drive has truly failed. If it's simply "Not detected", a three-foot drop test doesn't usually cause that kind of damage to a mechanical drive so as lhuser pointed out, you may need to open the bottom of the laptop and check the connection.
If you need to install Windows again, you have to have an install disk for Windows. You most likely have an OEM version of Windows on your Laptop so you will need an OEM installation disk. An installation disk is an installation disk when it comes to Microsoft, to an extent. If you install Windows from your friends "Retail" copy of Windows, your key won't work. If you install from your friends "OEM" copy of Windows, your key will work.
Now that you have Windows reinstalled, you need to reload any programs you had on the previous installation.
The next step might not even work but you can then try to inset your "recovery" dvd and restore the settings that were saved to that DVD. My guess, though, is that there are checks in place to make sure you put the right DVD in the drive. One of those checks might be an installation hash ID. If it does check this value, then it's going to see that you're trying to restore settings from a different installation and stop the operation.
HOPEFULLY though, it's a matter of a loose connection and inspection of the drive itself will reveal the need to simply push it back in. Good Luck