Depending on why the drive is not booting you can normally get files off by placing it in another computer.
You may need to take ownership of the folder containing the files first.
To take ownership you would do the following.
You need to take ownership of it.
Right click the drive OR folder and select properties. You will most likely be looking at your user folder.
From the windows that appears select Security(1). On that tab select Advanced(2).
A new windows will open....
Select the Owner(3) tab and select Edit(4).
From the next screen you can select your self as the owner(5) and make sure you check the "Replace owner on subcontainers and object"(6, make sure you check this, my image is not checked, but you want to check it) box.
Apply(7)