The easiest way to see if you can read your files or get them off your PC is to use a Low-Level access CD.
You will be booting from a CD that grabs the information of the operating system installed on the computer.
The program that I've used before in this situation is called ERD Commander. And you just have to download the .iso file and burn it to a CD and then boot from it.
You can do a search for ERD Commander or you can download from the following URL:
drsgeorgia.com/index.php/downloads.html
Once you boot from that CD you will be able to see your hard drive, if it's working. You will probably have to use a flash drive to move the files off of your old hard drive.
Also, you may attempting to delete files that you don't need on that old hard drive and then rebooting to see if freeing up hard drive space can help you at least get it booted.
If that works, there are some other tools within the above website that will help you free up even more space.