Restoring OS X to MacBook. How I overcame a forgotten password problem in the process.

I've been using a 13" MacBook (late 2009, 2.26 GHz C2D, 4GB RAM) for more than three years and it was starting to get uncomfortably slow.
Additionally, I was seeing just a little too much of that dreaded beachball.

While Onyx and iBoostUp helped marginally, I needed much more improvement in the performance of what has become my mainstay computer over the last few years.

Nothing for it but to wipe the hard disk and reinstall OS X.
Well, now that OS X features a recovery system, nothing could be simpler, right?

First, of course, I copied all of my important personal stuff, my iPhoto library, documents, music, my calibre library and others to a HFS+ formatted partition on an external hard drive.

Now, just reboot and hold down Ctrl-R during the boot up.
The first "recovery" option I chose was to delete the hard disk.
Well, I just wanted to make sure that absolutely none of whatever was slowing up my computer was remaining.
Next, re-install OS X (Mountain Lion).
So far, everything is going exactly as expected.

Then I'm asked to enter my Apple ID and password.
OK, that's easy.
However, I then get a message telling me that that was not the Apple ID I used to install Lion.
Really?
What's Lion got to do with it. I want Mountain Lion.
But I upgraded from Snow Leopard to Lion online and from there to Mountain Lion.
And this has not been forgotten.
Nevertheless, its relevance is still unclear to me.

However, the truth is that I have three Apple IDs that I've used over the years.
Two are regularly used and have known passwords.
The third, however, for reasons I just cannot explain, has an unknown password. Plus, none of the password recovery options work for this Apple ID. The password change options don't appear in any of my usual email addresses and the password recovery does not accept my DOB.

I honestly cannot explain what happened here.

In any event, of course it was the third Apple ID that was used to upgrade Snow Leopard to Lion.

So, now I'm stuck.
I've wiped my HDD and I can't reinstall Mountain Lion because I cannot use the Apple ID used to purchase Lion.
Oh boy.
Now what can I do?

Well, one option is just to buy Mountain Lion.
But wait, I have a Snow Leopard install DVD somewhere.
Let's install that just to have something to work with.
After the install, I then used the Applications Bundle DVD to install stuff like iPhoto and Garage Band.

Now do I have to install, and pay for, Lion?
Well, you can upgrade Snow Leopard 10.6.8 directly to Mountain Lion without having to go through Lion.
So, I just update Snow Leopard to the latest version which is very easy.

But wait, when I upgraded to Mountain Lion, I kept the Install Mountain Lion image and copied it to the external HDD.
So, copied it back to my Mac and started the upgrade to Mountain Lion.
This went without a hitch and I'm back where I started but with a HDD which is very much less loaded than it was previously.

And performance is very significantly quicker and smoother.
Nice job but must remember to write down all passwords in future.