I have a computer that I am de-commissioning which has Microsoft Office 2003 on it. I would like to move this software to the new computer which is replacing the old computer.

1. Can I do this or will the Microsoft Activation Process stop me in my tracks? I've already installed this software on three computers (3 user license).
2. Can I just swap this hard drive to the new computer and load the new drivers (video, LAN, etc.)? What do I do about the existing drivers that are no longer needed.

Lots of questions. Thanks for your help.

As long as you uninstall Office 2003 from the old machine you can install it on the new one. If you run into activation issues -- You can select the activate by phone option. To get the number to call microsoft and explain your situation to them and they will be able to help get your software activated.

Activate by using the telephone You can telephone an Activation Center and activate your product with the help of a customer service representative.

Important Telephone contact numbers vary by license and country/region. In step 2 of the Activation Wizard, use the number provided to call the Microsoft Activation Center. Activation Center telephone numbers are not listed in this article because the correct number for you is based on several factors. Microsoft software can be obtained under various licenses, including individual retail licenses, original equipment manufacturer (OEM) licenses, and volume licenses, so it is important that you use the number indicated by the Activation Wizard.

Telephone activation might take longer than activation through the Internet. You should be at your computer when you call, and you should have your software Product Key available.

In the Activation Wizard, select the country/region where you reside and where you plan to use the product.
The wizard provides one or more telephone numbers appropriate for your selection. Use the number provided on your Activation Wizard screen to call the Microsoft Activation Center.

Call the Activation Center.
The customer service representative asks you for your installation ID (displayed on your screen) and other relevant information. After your installation ID is verified, you receive a confirmation ID.

In the Activation Wizard, type the confirmation ID in the spaces provided at the bottom of the screen, and then press ENTER.

You can not swap your hard drive to the new computer and expect it to work. If you plan on using it as your main hard drive with your operationg system you will need to use windows file transfer wizard to backup all of your files onto another hard drive. Then you could move the old hard drive to the new computer and do a clean install of your OS onto it. You would then need to transfer all your files from the backup drive. You would also have to reinstall all of your other programs (Office and other programs you use).

Otherwise, if the new computer already has a hard drive and the OS installed you could take the old drive out of the computer and plug it into the new computer as a secondary drive and then, you could transer all your old files (documents, pictures, music, videos, etc.)over. Either way you would still need to install all of your programs (office and anything else).

A damn fine answer from kfawcett that will be much appreciated by many who don't quite know what's what with licences.

A damn fine answer from kfawcett that will be much appreciated by many who don't quite know what's what with licences.

Maybe not so fine. In theory, a 3 user license won't allow installing on a fourth computer, if that's what the OP is stating.
It's quite possible to use an old drive in a new machine using XP's repair install, but the OP didn't say what OS.
I had the same problem with moving Office, but I just put in the CD to see what would happen, and it worked just as it should have.