Usually, with an upgrade version it does not ask for a CD key, it asks for a CD. Also, they usually go back farther than they claim. For instance, the XP Upgrade disk says on the package that any version of Win 98, ME or 2k qualifies. But I used the Win 95 CD and it worked.
To install with XP you have to do a clean install. It doesn't let you upgrade directly from XP to Win 7. It will probably work like other clean installs using an upgrade disk. If you boot directly to the DVD (not CD anymore) with a clean hard disk it will ask you to insert the install disk that qualifies for the upgrade. In other words, you boot from the Win 7 DVD, and it will give a message that you must insert the XP CD. Once you insert the XP CD it will eject that and continue with the install. So, just having the XP key probably won't work. That is how previous upgrade disks have worked.
This isn't true. It was true for XP, but changed with Vista upgrades, and now 7. It won't ask for a disk, you need to have a valid XP/Vista installation on your target partition. There was a shortcut for fresh installs with Vista (basically install Vista w/o entering your serial, then reinstall with your upgrade key and it worked), but you need an installation on the target drive, even if you are doing a clean install.
You must have purchased the Windows 7 Home Premium Family Pack. The package includes two disks only. One that has the 32 bit version of Windows 7 and one that has the 64bit version. You do not get seperate disks for each install. Instead you use the appropriate bit version disk one each of the 3 computers you are upgrading. I recommend starting with the 64bit disk. Then if it says it isn't compatible try the 32bit disk.
@kalip I would get another upgrade of Windows 7 and upgrade both the laptop and the other system. Homegroup and the enhancements to Networking make it worthwhile to have all your systems running Windows 7.