I found the following instructions on the net that produced some sort of Product Key using a Linux based CD with a rudimentary registry editor and a Windows application KeyViewer. However my PC would not accept this Product Key as a correct one. I then ran KeyViewer on another XP system with a known Product Key and it produced an incorrect one again. I am going to copy the instructions here anyway, it's possible that keyviewer works only for certain versions of XP - Home/Professional, OEM/non-OEM etc or that another segment of XP registry has to be inspected.
Create bootdisk from the cd050303.iso
found here:
http://home.eunet.no/~pnordahl/ntpasswd/
Boot (dead) system using the bootdisk (CD)
*Note: BIOS must be set to boot from CD
1. Select disk where the windows installation is located. Generally this would be the first one listed (is also notated by Boot). Press '1' [Enter] to select the first drive listed.
2a) Enter path to the registry files. (Press [Enter] to select default)
2b) Select which part of the registry to edit. In this case, you want 'software' so type: software [Enter]
3. You should now see the loaded hives indicates <software>
Select '9' [Enter]
At prompt, do the following:
Type: cd Microsoft\Windows NT\CurrentVersion [Enter]
Type: hex DigitalProductId [Enter]
This will list the value of the DigitalProductId. Look for the line 0030.
Starting from the 5th column (following 00 00 00 00) write down the next
15x HEX code values (each set of 2 characters is a hex value).
You should end up with 30 characters, ending on the row beginning with
0040, in the 3rd column.
Eg. 7F6A514C8E5A9156EA34771AB7F202
Now that you have what you need, you can either just eject your CD and
shut down the dead PC, or shut down properly by typing:
q [Enter]
q [Enter]
n [Enter]
exit [Enter] (then wait for prompt)
Eject CD and shut down.
From either a boot floppy also containing the key viewer, or from a working system,
run KeyViewer which can be downloaded from here:
http://www.ac2tech.com/tools/keyviewer/keyviewer.php
Select the tab, 'Raw Key'.
Enter in the 30 character Hex code you wrote down (no spaces) and press the
Decode button. The Product Key will appear in the window below.