There is no technical reason that prevents you from using your laptop's hard disk in your desktop.
However, it is more than likely that the Windows 7 from your dead laptop is an OEM licensed version. That means MS doesn't allow you to use that Windows 7 license key in your current desktop PC. There are many more restrictions on how you are allowed to use an OEM licensed version of Windows, but I won't bore you with that.
Besides this, the hardware inside the laptop and desktop PC is very different. In general, most Windows installations that are transferred from one PC to another try to install whatever they need to copy with the hardware changes automatically...which usually results in such a mess that you need to re-install from scratch.
Transferring a hard disk with a Windows installation on it between computers with identical hardware (and that includes similar devices being connected at similar PCI (express) lanes) most of the time does work. But it is still something you are not allowed to do with an OEM licensed version of Windows.
Retail versions of Windows are much more expensive than OEM versions, but those are allowed to be installed on any one
(!) computer, such as a desktop or laptop.
You can find out which version of Windows you have by opening the Start menu and right-click on the 'My Computer' link inside that menu. A context menu should appear where you can select option 'Properties'. When you do that a window will open where you see the current Windows version (and service pack) near the top of this window.
Looks like you can still download XP Service Pack 3 from FileHippo
. Maybe there is still a forgotten corner in the Microsoft website where you can download SP3 for XP still, but by the time you find it there, you will likely have downloaded it from Filehippo in the background.
If you do add the laptop hard disk in your desktop PC, you shouldn't have to worry. According to this Wikipedia page
the core NTFS file system didn't change between XP and Windows 7. So you should be to access or write files on that hard disk without problems.