So I recently found out that my laptop harddrive is failing. I also have recently gotten a windows 8 key through dreamspark and installed W8 on my failing harddrive without knowing. Could I re-install windows 8 on a new harddrive using that windows 8 key without problems?

There are no absolute guarantees when you are dealing with operations at the most basic system level. However:
If you do a clean install to a new hard drive, you should be able to copy user files from the old to the new drive. Of the possible limitations, the possibility of the drives failure causing corruption is the dominant. Another is a small glitch having to do with file "ownership" In some circumstances you can get messages about inability to copy because you do not have ownership of the files. That is easy to fix by changing the ownership of the files. Of course, to copy user files from the old to new, both have to be installed drives. One can be in a USB-attached enclosure, for example. Applications would have to be re-installed.
With cloning, complications are few aside from the problems of drive failure of the old HD. If all goes well and there is no file corruption, applications and user files are already "there" and ready to go. Of course, the process of copying everything takes longer than just the OS install would.