While I'm pretty sure you mean GB and GHz respectively, I'm betting a new HDD would be the answer to your problem.
Apple Hardware Test is better than nothing, but it's HDD testing abilities aren't all that great, and since we're not dealing with a Windows system, malware is more or less out of the question. So, that leaves us with a failing HDD. In this case, it is likely in the rather early stages, and is just slow. Which is good, plenty of time to back things up and put in a new drive.
I believe Apple went all SATA when they shifted to Intel CPUs, so pretty much any 2.5" SATA drive should do the trick. Just do yourself a favor, and tape a piece of string or something in kind of a U-shape so you can pull the drive out again without removing the top case. Or if the replacement drive dies, you could just say it's time for you to get a new laptop, give your wife your current system.
I have a 2nd gen white Macbook (2,1) that my wife uses for only email and web search (I have moved on to Macbook Pro). Her Macbook is running very slowly. I've looked through these forums and found snippets of advice. I did the Mac Hardware Test, Extended Test, and it says nothing is wrong. There's 1mb RAM, a 2mb processor, and 59gb of storage left. She has only two programs at the most open at one time. I'm lost as to what's making it run slowly. Would bumping the RAM to 2mb help?