Laptops :: Reinstalling Tiger On Macbook - Hard Drive Dead?

I'm fairly new to macs and am having some problems. Here's the situation:

I've got a 3 year old 13" Macbook - 2.1 Intel Core 2 Duo, 1.83 Ghz, 512MB memory, 60 GB hard drive - I bought it from
Apple directly - it was a ""reconditioned"" one from the factory.

It has worked fine for 3 years, but lately has been getting slower and slower (most programs), and even the home screen has been acting weird, and loading up funny, if at all sometimes, and I get the "spinning beachball of death" much more often and/or for longer periods. I have all my files copied elsewhere, and I just figured I would start over and reinstall the 10.4 Tiger OS that came with it - I have the original grey install/restore DVDs.

In case it matters, the two install/restore DVDs read:
mac os version 10.4.8
AHT version 3AA18
disc version 1.0
22691-5967-A

So here's what I've tried so far:

-I booted up with the install/restore DVDs and have run the hardware checker several times. It says everything is fine.

-Also through the Utilities on the restore disk, i checked/repaired the disks and the "permissions" which showed up in the Disk Utility as the "Mac hard drive" or something like that, about 5 or 10 GB, and the main part of the drive, the "55.9 GB Fujitsu MHV2060BHPL". That all seemed to check out fine as far as the computer could tell me.

-I tried installing Tiger from the restore DVDs, the first time with the "archive and install" option. It seems like everything is working with the installation, and it gets through the second DVD, but when its done, it states that there are "software errors" and to try to install it again. (And no it won't boot up at all on its own...) I tried it again with another of the install options, I think it was "Erase and Install" - same thing. I also tried the "first time install option" too - same thing.

Next, since I got all my info off the computer already, I tried reformatting. First I used the function that writes zeroes over everything, for both the "Mac HD" and the "55.9 GB Fujitsu" drive too. Then I tried all three different install options again, starting with the "initial install" one. I also went into Disk Utility and used the format (and/or partition?) function and the drive has been redone with the mac os "extended journal" format, always with the same result as before. The whole thing (including the DVD test that it runs) seems to go fine with the install, but at the end it always says there are software errors and to try the install again... Is this possibly a hard drive problem (even though it "tests" fine)?

What if I ordered one of these:

Would that work in my macbook? Could I just replace the drive and go for another "first install"? Or is it likely something else?