Your issue is not that you can't find the image to download... your issue is assuming that you should be able to download it, and that it should be available for download.
Did Microsoft allow DigitalRiver.com to host the ISO files for XP, Vista, and Windows 7 ISOs? Yes. Were they freely available for everyone to download? No. Was it was possible to get hold of a link and download one of these ISOs? Yes. Are all these links still available on the internet somewhere? No.
Microsoft did want to allow some people to be able to download an ISO of their version of Windows, but Microsoft also believes they should be the ones to decide who should, and should not be downloading their OS. I'm not talking about the broad sense of the decision... I mean Microsoft wanted to be very specific about who they gave permission to/the ability to.
Since you are talking about using the key on the COA sticker on the bottom of the laptop, you are talking about an OEM installation (as opposed to a Retail installation... it makes a difference). You won't be able to use a Windows XP Pro Retail ISO with that product key. So, although I won't violate any laws with links, I can tell you that you can take your chances on the bittorrent circuits, and search for a Windows XP Pro OEM ISO. You don't want one that is pre-activated, or comes with a crack or a hack. You just want an untouched ISO. You might get lucky.
You can also contact the manufacturer of the laptop (Via their Support web site) and request to purchase the recovery media for that model laptop. Purchase? REALLY? OMG, you just want the OS! Yes... I know this. And, you won't be spending $100 or $200 by going to the manufacturer. You'll spend between $10 and $40 for their recovery discs, which will include the original OS that was shipped with the laptop... providing they still have them. Remember, we are talking about Windows XP here. The OS that was replaced by Vista... that was replaced by Windows 7... that was replaced by Windows 8.
As a last resort, you could contact Microsoft directly... but the chances are great they are going to tell you that they cannot and/or will not assist you... and they will just attempt to sell you a copy of Windows 8.