Failed Hard Disk

I turned on my desktop a few nights ago and decided once and for all, I was going to defragment the hard drive. It had been forever since it was done (possibly as long as a year). Disk Defragmenter likes at least 15% free disk space. I had about 12%. I decided to bite the bullet and clear off a bunch of stuff I really didn't need so it could do a complete and proper defragmentation of the drive. After several hours, I got it where it needed to be. I ran the process and let it go until it was done.

The next morning, I turned on my computer to check and see if it was any faster. As it was booting, I walked out of the room to do a few things. I came back and noticed that although every was up and running, the computer was running very sluggish. Everytime I tried to open a program or access any files, it would load very slowly. A few programs crashed randomly too. I knew it was something serious, and I knew it was definitely not a virus. What I feared became a reality -- upon restarting it, it wouldn't even boot up all the way into Windows because it said a directory needed by the operating system was missing.

Today I went out and bought myself a new hard drive. It's much bigger than the old one (500GB as opposed to 80GB). I haven't put anything on it yet, but I'm really hoping after I get the operating system loaded on there, I can access the files from my old hard drive and move them over. I've had hard drives malfunction and go bad, but I was always able to access files from them. This situation is different as the drive really seemed like it was dying a very painful death judging by the inability to read some very basic stuff from the drive. I backed up some of the important things, but not everything. I would like to keep as much as possible, and that is the big upcoming test I face.

Does anyone have any suggestions of what I should do?