Oh this is an easy one.
1. Open your My Computer and browse to your Documents and Settings folder
(c:\documents and settings\[your_user_name])
2. Locate the favourites folder and open it.
3. There will be lots of files within this folder, this is all your
favourites.
Right-click and send them to CD to be written (should be in the Send To)
If you cant send them to the CD, then right click copy and paste it into
the CD or drag them onto the CD icon in My Computer.
4. Write files to CD and thats them backed up.
To recover these files, just do the same process up to 3, but instead of
copying to the CD, copy from the CD onto your new account for your new HD.
All your favourites should be sitting nicely in your new IE favourites.
There is programs that could do this, but its easier in your situation to do
this since your HDD is dying.
I have went through the same process as you... it sucks.
Although i was one step futher along the dying process cause i backed up
using DOS and a zip drive. Fun times!
Hope this helps you and good luck with it
-kris-