Before I get started, here is the finished product from the hardware swap.

Part 2 – Loading the OS
If you have an external DVD drive, hook up the drive to the Eee PC prior to booting up.

Step 1.  Power up the dvd drive and insert the Asus Eee PC 1000H Recovery DVD.

Step 2.  Power up your Eee and press Esc.  Don’t stop until the system ask you what drive you want to boot from.

Step 3.  The system will load a Windows Staging environment from the DVD as it copies the factory image of the OS to your Hard Drive.  They system uses Symantec Ghost to re-install the hard drive image.

Step 4.  The system will stop and ask you how you want to set up the hard drive partition.  After you make your selection, follow the on screen directions until Windows is completely installed.

Note, you make have to reboot a few times.  After this, Windows should be up and running on your new Hard Drive.

If you do not have access to an external DVD drive, there is a way to load the OS through a USB key.

Here’s what you’ll need:

Asus Eee PC 1000H Recovery DVD
A PC running Windows XP or Vista with a DVD drive and WinRAR installed.
A 4 GB USB Flash Drive
This website:  http://myeeeguides.wordpress.com/2008/10/15/eee-pc-1000h-recovery-from-usb-flash-drive/

I can’t take credit for this.  I found a very good guide that walks you through makiing a bootable flash drive.  It’s a very easy and good guide.