It sounds like that wasn't any branded disk but one the custom builder included since that was the one for the preinstalled OS seen there. Without the original disk in order to perform a repair or full reinstall of XP there you would need a totally new disk onhand.
MS won't replace any disk free simply due to you losing it. That's your headache to them! For obtaining a new license they will readily sell that however. The original builder being "Out of Business" otherwise means you simply buy a new full install disk to use with a totally different product number to start over with.
Simply recovering the product key for a disk you no longer have won't do anything for you. For a Dell, HP/Compaq, Gateway, or other prebuild a rep dealer will simply use the serial number on that particular system to order a replacement recovery disk set that should see all prepackaged softwares included for a prce there.